For general reference or interest, I thought I'd gather into one place as many of the Old English words lurking in Tolkien’s writings as I could think of. Some you’d expect; others might surprise or interest you. Some might seem more or less intentional on Tolkien’s part--as an Anglo-Saxon scholar, he would at the very least have been aware of their meanings, and therefore aware (and perhaps glad) of the “coincidence” (if such it be) between the meaning and his use. In some instances Tolkien has explicitly noted the connection somewhere (LOTR appendices, his letters, elsewhere). Of the names of people of Rohan, I've only included what I thought were the most interesting or relevant or original. (Most of them are simply historically documented Anglo-Saxon names anyway.)
Standard abbreviations are used: OE=Old English, ON=Old Norse, ModE=Modern English, OHG=Old High German, ROTFLMAO...you get the picture.
Beag: ‘ring’. In the Mercian dialect (which Tolkien used for the Rohirrim), I think this would have been spelled bag; either way, pronounced almost like modern English ‘bag’. Remind you of the last name of any hobbits you know?
Beorn: ‘man; noble, hero, chief, prince, warrior’; however, this is also how OE would render ON bjorn, ‘bear’.
Brego: ‘ruler, chief, king, lord’.
Deagol: diegol, deagol, ‘secret; hiding place; grave’, akin to diegan, ‘to die’. So if Smeagol is one who digs (see below), Deagol recalls all sorts of aspects of his relationship to Smeagol: the death he caused, the grave he dug, and that which he kept hidden and secret (this last meaning is referenced by Tolkien in LOTR, Appendix F).
Dwarrowdelf: dweorg, ‘dwarf’ (akin to German zwerg, Old Norse dvargr) + ‘delf’, an archaic noun formed from ‘to delve’, hence, ‘the delving of the Dwarves’, or ‘dwarvish digging’.
Dwimorberg: dwimor, ‘phantom, ghost, illusion; error’ + beorg, ‘mountain, hill’.
Dwimordene: dwimor + dene, ‘valley, dale’.
Dwimmerlaik: dwimor (see above) + loga, ‘liar, deceiver’ (akin to ‘warlock’).
Emnet: ‘[geographic] plain’.
Ettenmoors/Ettendales: eoten, ‘giant, monster, enemy’ (sometimes confused with Eotenas, ‘Jutes’) + mor ‘moor, morass, swamp’ or + dæl, ‘dale, valley, gorge, abyss’.
Grima: ‘mask, helmet; ghost’. Perhaps Wormtongue was a mask or ghost of his former self; or perhaps he was a mask for Saruman’s influence in Rohan. Either one works.
Hasufel: hasu, ‘dusky, grey, ashen’ + fell, ‘skin, hide’.
Isengard: isen, ‘iron’ + gard, geard, ‘place, realm, ward, enclosure, yard, garden’ (hence middangeard, “middle-earth”).
Mathom: maðom, ‘treasure’; although ironically in the Shire they were no longer seen as treasures but as useless oddities to be given away (like today's fruitcake, I suppose).
Meduseld: medu, ‘mead’ + seld, ‘hall’. As we know from Beowulf and elsewhere, the meadhall is the standard place for the king to feast with his kin and dole out gifts and entertain guests.
Michel Delving: micel, ‘great, big,’ hence Scottish ‘muckle’. So the name signified a great digging or dug area.
Mirkwood: mircwudu, ‘dark forest’. In Norse poetry the term referred to the vast expanse of primeval forest in Germanic areas of the Continent.
Mundburg: mund, ‘protection, trust, security, the king’s peace’ (hence names like Edmund) + burg, byrig, ‘fortified dwelling, walled city’ (hence the –burg, –bury, and –borough endings of English place names). So Mundburg would be the city that symbolizes safety and security, with a royal connotation.
Orthanc: ‘intelligence, understanding, cleverness, skill, mechanical art’ (akin to OHG urdank). Isn’t this precisely the (downward) progression that Saruman’s mind underwent?
Quickbeam: cwicbeam, ‘aspen, juniper’.
Riddermark: mearc, ‘mark, sign, line of division; an area thus defined: boundary, district, province’ (possibly akin to the name Mercia). So the Riddermark is the district of the Riders (with the vowel in 'rider' shortened), just as Denmark is the district of the Danes.
Rivendell: reofan, ‘to rend, break’ (akin to ModE ‘rift’) + dell, ‘vale, hollow, dale’. So, a valley formed from the rending of stone (either naturally or otherwise).
Saruman: searo, searu, ‘clever, cunning’.
Scatha: sceaða, scaða, ‘criminal, assassin; fiend, devil’.
Shadowfax: sceadu, ‘shadow’ + feax, ‘hair’. (Compare Fairfax.)
Simbelmyne: simbel, simle, ‘ever, always’ + myne, ‘mind, remember’.
Smeagol/Smials: smygel, ‘retreat, burrow’. Hence, a ‘smial’ could be a modern descendant of this word, while *smeagol might indicate one who burrows or digs.
Smaug: Could be related to either (or both) of smygel (see previous entry) or smoc, ‘smoke’.
Theoden: þeoden, ‘king, ruler’, akin to þeod, ‘people’; Þeoderic (Go. Þiudareiks, Norse Þidrek, Germ. Dietrich), name meaning ‘ruler of the people’; and þeodisc, ‘of our own people’, akin to teutisch, the old form of deutsch, ‘of the German(ic) people’.
Warg: wearg, ‘wolf, outlaw’, akin to Norse vargr.
Withywindle: wiðig, ‘willow’ + windel, ‘basket’. So the Withywindle river valley was like a big basket of willows.