Gār‐Dena

The 'Gār‐Dena' are the 'Spear-Danes' from line one of Beowulf. All the translations I have read translate the name as 'Spear-Danes', which has a suitably tough-looking OE feel. But I was wondering: does it actually mean Germans? Can't find evidence to support it. The OED notes that 'Deutsche' and its cognates are ancient ('from the Old High German word diutisc -- diot "people"') but that the English didn't start calling them Germans until the 16th-century or later. 'Germans', of course, is from Tacitus' Germania. But where did that come from? Was it picked up from one of the German tribes themselves, who called themselves the Spear-folk, the 'Gār‐Diutisc' or Spear-men, 'Ger-menn'? I daresay there are endless dusty tomes already in the libraries arguing this thesis, or disproving it. But it gives me the chance to retranslate the opening lines of Beowulf:

Hwæt! Wē Gār‐Dena in geār‐dagum
þēod‐cyninga þrym gefrūnon,
hū þā æðelingas ellen fremedon.
Oft Scyld Scēfing sceaðena þrēatum,
monegum mǣgðum meodo‐setla oftēah.
Egsode eorl, syððan ǣrest wearð
fēa‐sceaft funden: hē þæs frōfre gebād,
wēox under wolcnum, weorð‐myndum ðāh,
oð þæt him ǣghwylc þāra ymb‐sittendra
ofer hron‐rāde hȳran scolde,
gomban gyldan: þæt wæs gōd cyning!

Hey! We've heard of the Germans of years-gone-by,
all their great kings, and splendid stories,
how those athelings earned their fame.
Scyld Scefing was skilled at scattering enemies!
He crushed many clans and many mead-settlements,
undid all those earls. Since from the first he was
found to lack funds, he fell back on friendship, and
grew great with welcome, thrived on his own worth,
until everyone who lived in that land, and
over the whale-road too all of them knew him,
offered him fealty. He was a good king!