Apparently there is some doubt here that "Wat" is a genuine English name.

It is true that it is not common among the upper classes. It was a lower class name. But it is widely attested. Examples:

The most famous "Wat" in history was surely Wat Tyler (killed 1381): "The most famous leader of the Peasant's Revolt in 1381, Tyler was a man of obscure origins. He may have worked as a tiler in Essex; he was said to have served with Richard Lyons, a wealthy London merchant in France.... He first emerged as a major leader in Kent at the end of the in June 1381, seizing Canterbury on June 10 and heading the march to London on the next day. On June 15 he was the spokesman at Smithfield.... The young king Richard II ordered the mayor [of London], John Walworth, to arrest Tyler, and in a struggle he was killed." (John Cannon, editor, The Oxford Companion to British History, 197; revised edition, Oxford University Press, 2002; entry on Wat TYLER.)

There is a poem in Richard Hill's commonplace book (Balliol MS. 354), generally believed to be a traditional religious song, usually known as "Jolly Wat" or "The Jolly Shepherd Wat." It opens:
The sheperd vpon a hill he satt,
He had on hym his tabard & his hat,
His tarbox, hys pype & and hys flagat;
Hys name was called joly, joly Wat;
For he was a gud herdis boy,
            Vt hoy!
For in his pype he made so mych joy.
Can I not syng but hoy
Whan the joly sheperd made so mych joy.
From Roman Dyboski, Songs, Carols, and Other Miscellaneous Poems from the Balliol Ms. 354, Richard Hill's Commonplace Book, Kegan Paul, 1907, item 30, pp. 16-18, leaf 224 in the actual manuscript. The original contains some abbreviations which Dyboski expanded; if anyone actually cares, I can list what they are. Hill collected his material in the reign of the Tudors, starting around 1500 and ending around 1536.

In the General Prologue to Chaucer's Canterbury Tales (lines I.642-643 as numbered in the Variorum Chaucer) we read
And eek ye knowe wel how that a jay
Kan clepen 'Watte' as wel as kan the pope.
In other words,
And also you know well how that a jay
Can call 'Wat' as well as can the pope.
(There are a whole bunch of manuscript variations in those lines, especially in 642, but Hengwrt and Ellesmere agree on the text, and the only variation in Gg is that it omits "how" in 642. And if that statement makes no sense -- ignore it; it's merely more scholarly apparatus.) As for what this means, it's in the description of the Summoner. The interpretation given by Morris in 1874 is that "the jay 'can call Walter (Wat) by his name; just as parrots are taught to say 'Poll.'" Mann in 1973 amplified that this is a traditional satiric form in which a "talking bird... is trained to repeat material beyond his comprehension." In other words, the Summoner parrots the words of his summonses.

So there we have it, from (in effect) three levels of English society: the poor (Wat Tyler), the urban commercial class (Richard Hill was a grocer who collected material from other businessmen), and the aristocracy (Chaucer, born a vintner's son, because a minor member of the gentry who wrote for the nobility). All attest the name "Wat."

I could offer additional information, but I suspect that you all stopped reading long ago anyway. :-) I can't even really say that I blame you. :-)