Of his cognomen, Tolkien wrote the following note:
My name is TOLKIEN (not –kein). It is a German name (from Saxony), an anglicization of Tollkiehn, i.e. tollkühn. But, except as a guide to spelling, this fact is as fallacious as all facts in the raw. For I am neither ‘foolhardy’ nor German, whatever some remote ancestors may have been.” 
Here we have Tolkien’s typical sense of philological humor, as the German tollkühn, of course, means “foolhardy” in English. It’s a compound, actually; just as “foolish” and “hardy” are more or less antonymic in English, so are German toll “mad, crazy” and kühn “bold”. Tolkien puns on his own name in The Notion Club Papers with the invention of Rashbold — so far as I know, unattested as an anthroponym, but actually attested as an English calque for Germanic dummkúhn “foolhardy, rash, rashbold, temerarious”.  I wonder whether Tolkien knew this (apparently unique) source!
But though this was Tolkien’s sense of his own name, was it correct? Could there be another explanation? It’s a somewhat strange, almost denigrating meaning, isn’t it? But even so, I would never have questioned this etymology had I not come across a rather arcane volume called The Teutonic Name-System Applied to the Family Names of France, England, and Germany. This surprising treasure trove takes a topical / etymological approach to anthroponymy, with introductory chapters on simple forms, diminutives, phonetic additions, patronymics, compounds, and so forth; followed by more fascinating chapters on Our Natural Enemies, The Brute and Its Attributes, The Gods of the North, and The Station in Life, among many, many others. In a chapter called The Warrior and His Arms, we find the surname Tolkien attested, like so:
The following root seems to be referable to Old Norse dolgr, foe, Ang.-Sax. dolg, vulnus [Latin “wound, injury”]. SIMPLE FORMS. Old Germ. Tulga (West Gothic king, 7th cent.), Tulcho. Eng. TULK. Mod. Germ. DULK. PHONETIC ENDING. Old Germ. Tolcon, 10th cent. Eng. TOLKIEN, TOLKEN. Mod. Germ. DULCKEN. 
As a side note, is the similarity between the names Tolkien and Tulkas a mere coincidence? Probably, but it’s tantalizing fodder for wild theories nonetheless! ;)
Does it make more sense for the etymology of one’s surname to refer to foes, weapons, wounds, and so forth, than to a state of foolhardiness (by which attitude I suppose one might have acquired more than one’s share of wounds, hahae)? I don’t know. Was Robert Ferguson right about its origins (e.g., he does not explain, merely asserts, the arrival of the –n)? Again, I don’t know. But it is interesting to see the name attested, on record, and with a very different etymology. Would that I could ask the Professor about it. I am sure it would have made for a very lively discussion!
 Tolkien, J.R.R. The Letters of J.R.R. Tolkien. Selected and edited by Humphrey Carpenter. Boston: Houghton Mifflin, 1981, p.428.
 Ibid., p.218.
 Bailey-Fahrenkrüger’s Wörterbuch der Englischen Sprache. Zwölfte Auflage, gänzlich umgearbeitet von [Twelfth edition, completely reworked by] Adolf Wagner. Jena: Friedrich Frommann, 1822, p.182.
 Ferguson, Robert. The Teutonic Name-System Applied to the Family Names of France, England, and Germany. London: Williams & Norgate, 1864, p.184.