All the variants of Germanic runic writing are basically kindred and go back to the Common Germanic Elder Futhark. One may be certain that these ancient runes had names. Alas, no rune-master of the Common Germanic period either left us a list of names for the Elder Futhark or explained what these names meant. Therefore modern expositions of the original rune-names and rune-meanings are more or less daring reconstructions (for the list of reconstructed names see this post). There are several sources that allow us to speculate about the Common Germanic names of runes:

• Anglo-Saxon runica manuscripta (the earliest late 8th century)
  
• Abecedarium Nordmannicum (9th century)
• Letter-names of the Gothic alphabet (recorded in the 10th century)
• Anglo-Saxon Rune Poem (end of the 10th century)
• Norwegian Rune Poem (late 12th century)
• Icelandic Rune Poem (15th century)

As one may see, the sources are rather late. Each of them is a witness of the contemporary runic tradition as it existed in a certain locality with respect to the number of runes, their meanings and names. Runica mansucripta are insular and continental manuscripts containing listings of Anglo-Saxon runes with more or less accurate roman equivalents and sometimes rune-names. One should remember that the manuscript tradition is somewhat different from the epigraphical one (whether or not they should be treated separately or combined as supplementary is not certain). Abecedarium Nordmannicum is a list of runes with short explanatory notes found in the Codex Sangallensis 878 that probably comes from Fulda. It is written in Old Saxon with traces of Anglo-Saxon influence. Names of Gothic letters are known from ms 795 from Vienna, National Library. The language of these letter-names is notoriously different from that of Ulfila’s translation of the Bible. Many researchers doubt whether this material may be relied upon. Anglo-Saxon Rune Poem from British Library MS Cotton Otho B.x has 29 stanzas of alliterative verse and is a very detailed account of the names and meanings of runes. Its Norwegian and Icelandic counterparts are shorter since they describe the 16-runes Younger Futhark and were recorded considerably later (for names and meanings of the Younger Futhark runes see this post).
Below is the list of Anglo-Saxon runes with brief notes as for their relation to other runic traditions. Each rune is accompanied by a verse from the Anglo-Saxon Rune Poem in 1915 translation by B. Dickins.

feoh, ‘wealth’. Both Norwegian and Icelandic Poems give fé, ‘wealth’. Gothic letter-name is fe.

Wealth is a comfort to all men;
yet must every man bestow it freely,
if he wish to gain honour in the sight of the Lord.

ur, ‘aurochs’. Norwegian Poem has úr, probably ’slag’, Icelandic has úr translated by Dickins as ’shower’. Which Germanic form gave all these attested names is not certain, since some or all of them altered the original meaning of this rune-name. Name of the Gothic letter is uraz.

The aurochs is proud and has great horns;
it is a very savage beast and fights with its horns;
a great ranger of the moors, it is a creature of mettle.

ðorn, ‘thorn’. Norwegian and Icelandic Poems have þurs, ‘giant’. Gothic letter-name is thyth. The name was probably changed due to Christian influence.

The thorn is exceedingly sharp,
an evil thing for any knight to touch,
uncommonly severe on all who sit among them.

os, ‘god’, probably Woden (ON Óðinn), who, according to Norse tradition, was skilled in speech and poetry. Dickins prefers to interpret os in the Runic Poem as the Latin word for ‘mouth,’ which could be a late introduction.

The mouth is the source of all language,
a pillar of wisdom and a comfort to wise men,
a blessing and a joy to every knight.

rad, probably ‘horse-riding’. Latin glosses for this name are equitatio and iter. Relation with ON reiði, ‘equipment’ is also possible.

Riding seems easy to every warrior while he is indoors
and very courageous to him who traverses the high-roads
on the back of a stout horse.

cen. This word is not known in OE beside the listings of runes. Probably means ‘torch’ or specifically ‘torch of pine-wood’ (cf. OHG chien, chen, ken). Latin gloss is facula. In Norwegian and Icelandic tradition this rune is called kaun, ‘ulcer, sore’. Abecedarium Nordmannicum gives chaon. Gothic letter-name is chozma.

The torch is known to every living man by its pale, bright flame;
it always burns where princes sit within.

gyfu, ‘gift’. Gothic letter-name is geuua. In Younger Futhark there is no such rune, so Scandinavian Rune Poems have no corresponding name.

Generosity brings credit and honour, which support one’s dignity;
it furnishes help and subsistence
to all broken men who are devoid of aught else.

wynn, ‘joy’. Gothic letter-name is uuinne. No Scandinavian name.

Bliss he enjoys who knows not suffering, sorrow nor anxiety,
and has prosperity and happiness and a good enough house.

hægl, ‘hail’. Gothic letter-name is haal. Scandinavian name is hagall.

Hail is the whitest of grain;
it is whirled from the vault of heaven
and is tossed about by gusts of wind
and then it melts into water.

nyd, ‘need, oppression, affliction’. Corresponding Gothic letter has a strange name nooicz. Scandinavian tradition gives nauðr, ‘constraint’.

Trouble is oppressive to the heart;
yet often it proves a source of help and salvation
to the children of men, to everyone who heeds it betimes.

is, ‘ice’. Scandinavian ís, Gothic iiz.

Ice is very cold and immeasurably slippery;
it glistens as clear as glass and most like to gems;
it is a floor wrought by the frost, fair to look upon.

ger, ‘year’. Scandinavian ár, Gothic gaar.

Summer is a joy to men, when God, the holy King of Heaven,
suffers the earth to bring forth shining fruits
for rich and poor alike.

eoh, also ih, ‘yew-tree’. There is no such rune in the Younger Futhark, but the R-rune has the cognate name ýr.

The yew is a tree with rough bark,
hard and fast in the earth, supported by its roots,
a guardian of flame and a joy upon an estate.

peorð, meaning unclear. The context of the Anglo-Saxon Rune Poem is the only basis for interpretations.

Peorth is a source of recreation and amusement to the great,
where warriors sit blithely together in the banqueting-hall.

eolhx, also iolx, ilx, ilcs, ilix, meaning unclear. In the Anglo-saxon Futhorc this rune was used as the equivalent of the roman x, since OE did not have the sound designated by eolhx in the Elder Futhark. Usually associated with Goth. alhs, ’sanctuary’, supposed Common Germanic form is *algiz, ‘protection’.

The Eolh-sedge is mostly to be found in a marsh;
it grows in the water and makes a ghastly wound,
covering with blood every warrior who touches it.

sigel, ’sun’. Scandinavian sol, Gothic sugil.

The sun is ever a joy in the hopes of seafarers
when they journey away over the fishes’ bath,
until the courser of the deep bears them to land.

tir, ‘Tiw’. In Common Germanic it was the name of a god, in the Anglo-Saxon Runic Poem it is probably a name of a star or constellation named after the god.

Tiw is a guiding star; well does it keep faith with princes;
it is ever on its course over the mists of night and never fails.

beorc, ‘birch-tree’. Gothic letter-name is bercna. Dickins prefers to translate poplar since Latin populus occasionally glosses beorc.

The poplar bears no fruit; yet without seed it brings forth suckers,
for it is generated from its leaves.
Splendid are its branches and gloriously adorned
its lofty crown which reaches to the skies.

eh, ‘horse’. No Scandinavian name, Gothic eyz.

The horse is a joy to princes in the presence of warriors.
A steed in the pride of its hoofs,
when rich men on horseback bandy words about it;
and it is ever a source of comfort to the restless.

man, ‘man’. Scandinavian maðr, Gothic manna.

The joyous man is dear to his kinsmen;
yet every man is doomed to fail his fellow,
since the Lord by his decree will commit the vile carrion to the earth.

lagu, ‘water’. Scandinavian lögr, Gothic laaz.

The ocean seems interminable to men,
if they venture on the rolling bark
and the waves of the sea terrify them
and the courser of the deep heed not its bridle.

Ing, ‘the hero Ing’. No Scandinavian name. Gothic enguz.

Ing was first seen by men among the East-Danes,
till, followed by his chariot,
he departed eastwards over the waves.
So the Heardingas named the hero.

eþel, ‘land, landed property’. No Scandinavian name. Gothic utal.

An estate is very dear to every man,
if he can enjoy there in his house
whatever is right and proper in constant prosperity.

dæg, ‘day’. No Scandinavian name. Gothic daaz.

Day, the glorious light of the Creator, is sent by the Lord;
it is beloved of men, a source of hope and happiness to rich and poor,
and of service to all.

ac, ‘oak-tree’.

The oak fattens the flesh of pigs for the children of men.
Often it traverses the gannet’s bath,
and the ocean proves whether the oak keeps faith
in honourable fashion.

æsc, ‘ash-tree’.

The ash is exceedingly high and precious to men.
With its sturdy trunk it offers a stubborn resistance,
though attacked by many a man.

yr, meaning unclear.

Yr is a source of joy and honour to every prince and knight;
it looks well on a horse and is a reliable equipment for a journey.

iar, also ior, meaning unclear.

Iar is a river fish and yet it always feeds on land;
it has a fair abode encompassed by water, where it lives in happiness.

ear, probably ‘grave’.

The grave is horrible to every knight,
when the corpse quickly begins to cool
and is laid in the bosom of the dark earth.
Prosperity declines, happiness passes away
and covenants are broken.