I have no idea exactly what relationship the Saxons had with their names, and I don’t know what academic work has been done on it—I’m just going on the impression I get from the names themselves—but the names are often easily parseable into combinations of words. Rather than take them from a literary source like Beowulf, here’s a list of names found in a poem which was about fairly contemporary events, The Battle of Maldon. The spellings are adapted somewhat to be closer to modern English pronunciation; i.e. ‘Æscferð’ becomes ‘Ashferth’, ‘Æþeric’ becomes ‘Atherich’.
Offa, Eadrich, Byrhtnoth, Athelred, Wulfstan, Ceola, Maccus, Alfere, Byrhtelm, Wulfmar, Alfnoth, Godrich, Godwin, Godwig, Alfwin, Alfrich, Ealhelm, Leofsunu, Dunnere, Edglaf, Ashferth, Atherich, Sibirht, Gad, Wistan, Thurstan, Wigelm, Oswold, Eadwold, Athelgar.
Now if I say that athel* means ‘noble’ and gar means ‘spear’, it looks an awful lot like ‘Athelgar’ means ‘noble spear’. Here are some other bits of A-S vocab so you can pay along at home:
ash – ash (the type of tree)
byrht – bright
ead – rich, blessed, happy
edg – edge, sword
ferth – soul, spirit, mind
god – good, God
helm – helmet
leof – desirable, pleasant, loved, a friend, a loved one
laf – what is left, remnant
noth – boldness
rich – power or powerful
sunu – son
stan – stone
wulf – wolf
So what happened to all these meaning-full names? Well, the Norman Conquest, basically. Skip forward a couple of centuries and despite English remaining in continuous use, very few of the old English names hung around. A few, mainly associated with saints and kings, are used to this day: Alfred, Edward, Edmund, Harold and Oswald must be the most common, but you occasionally meet a Godwin, Cuthbert or Dunstan.
By the 16th century, about 30% of men were called John, with another 40% called Thomas, William, Richard or Robert. And I believe they were generally named after their godparent, so there wasn’t much room for creativity there. And of the top 50 mens’ names from the 1560s and 1570s on this page, only two, Edward and Edmund, are of English origin rather than French or biblical.
Actually, it’s quite interesting that the Anglo-Saxons didn’t use Bible names; they’d been Christian for several hundred years by the time of the Battle of Maldon.
I doubt if we’re going to have a revival of these names any time soon; most of them sound distinctly harsh to the modern ear. I rather like Ælfric (i.e. Alfrich); apart from the sound of it, there was a man called Ælfric who was a grammarian, translator and hagiographer. According to Bosworth and Toller, ælf is ‘elf, genius, incubus’, so ‘Aelfric’ must be something like ‘elf-power’. Powered by elves? With the power of an elf?
And since ræd means ‘advice, counsel’, Alfred means ‘elf-advised’. That’s the joke in the name Ethelred the Unready, of course. He was Æthelræd Unræd— his name, Æthelræd, means ‘advised by princes’ or ‘noble advice’ and unræd means ‘ill-advised’. So called because it was on his watch that the Danes took over half of England.
*again, strictly speaking that would be æðel. I’m not going to footnote my spelling every time, but similar tweaks apply throughout.