Mine, Mine, Minefield
When I write program notes, or as I am doing presently, edit scores, the question arises: How to spell the name of the beloved Saxon, that accomplished composer and wildly successful 18th century businessman, the greatest German ever to bring Italian opera to the British. How should we spell Handel? Er… Händel. I mean, Hendel.
To be clear, I write from an Anglo-centric (specifically American) perspective. This is an important point to make, as the question of spelling arises not just because George Frideric (er… Georg Friederich) himself adopted multiple spellings throughout his lifetime, but because several nations lay claim to his musical legacy – local boy done good, etc…
“No alien musician ever more quickly saw what the people of this country required or so promptly qualified himself to supply it. A German among the Germans, and an Italian among the Italians, Handel was an Englishman among the English and, if anything, bettered his model.” 
Unlike similarly diacritically challenged composers, such as Dvořák and Kodály, we want to spell Handel’s name in a way that highlights his link to our people.
You Put a fpell on Me
Determining a standardized spelling for the English language is a somewhat recent preoccupation. In 1754, 150 years after the publication of the first alphabetical English dictionary (previous dictionaries were ordered by subject headings), Philip Stanhope, the 4th Earl of Chesterfield, lamented:
“…it is a sort of disgrace to our nation, that hitherto we have had no… standard of our language; our dictionaries at present being more properly what our neighbors the Dutch and the Germans call theirs, word-books, than dictionaries in the superior sense of that title.” 
The first reliable English dictionary, A Dictionary of the English Language, was produced the following year by Samuel Johnson. The Oxford English dictionary was compiled over the course of fifty years beginning in 1884, Noah Webster having published his own A Compendious Dictionary of the English Language and An American Dictionary of the English Language in 1806 and 1828 respectively. These men did not seek to simply record an already standardized system of spelling, rather, they worked to codify and streamline a mess of potential choices. Thanks to Webster, for example, Americans now write color rather than colour, center rather than centre, and we would not be caught dead in a theatre.
Handel was born into a world that cared much less than we do today about both spelling and the past. We are burdened with the desire to not only ‘own’ the man for our national identity (and there are few things less Anglo than an umlaut), but to give the man as historically accurate a name as possible. Much of the revival that brought his music to present day audiences was based on giving the most historically informed reading of the score possible. Why not start with the title page, right? So, with our scholarly hats on (a rather HIP look, no?) what does the record suggest?
Mr. Handel was definitely baptized Georg Friederich Händel in 1685 (figures 1 & 2). 
Upon matriculating at Halle University, he signed his name George Friederich Händel in the student register (figure 3). 
While living in Rome, Handel signed his name G.F. Hendel (figure 4) in 1706  and did so again in the 1707 autograph of his Dixit Dominus (figure 5). 
Upon moving to England, he began spelling his name Handel (the aglicization of one’s name being a common practice among immigrants – see Ellis Island), culminating in his application for British citizenship in 1726 under the name George Frideric Handel (figure 6). 
The trail, however, does not go dead there, as this 1743 title page to the Libretto for a performance of Messiah gives yet another spelling of his middle name (figure 7). 
If, however, we ignore subtle variations to his middle name, a strong case can be made that Handel intentionally adopted the English spelling of his first and last names, and continued in this manner for the rest of his life. Mr. William H Cummings, Esq., laid the case before the Royal Musical Association in the 1880s:
“We find that when Handel went to Italy he spelt his name Hendel; but when he came to England he seems immediately to have substituted the a for e, and he wrote himself down as Handel… That Handel adopted this mode of spelling with intention is further shown by his petition to the House of Lords [his application for British citizenship]… in which he twice spells his name Handel. In his oratorios he frequently subscribed his name and the date of composition: in these instances he always spelt it Handel; and to come to the last act of his life–the making of his will–here again he spelt the name Handel… If Handel was so anxious to make himself an Englishman, surely we ought not to be anxious to denationalize him… I should add that Handel, in writing to his own family from England, and writing in German (even to his mother), spelt his name Handel.” 
Handel, Flexible with Purpose
While it appears that Handel was flexible about the spelling of his name throughout his life, he was not arbitrary in his choices. Ever the astute businessman, he blended into England as best he could. He was successful, at least in part, because the English felt that he was one of their own. Unlike his time in Italy, when he was known as the beloved Saxon (caro Sassone), Handel seems to have adopted England as thoroughly as England adopted him.
Curiously, the Italian spelling “Hendel” (when spoken by an Italian) results in much the same sound as the German “Händel” (both are open e sounds [ε] like bed, spread, fed, etc…) That spelling choice could very well have been motivated by a desire to trick the Italians into approximating the German pronunciation. I have found no evidence that 18th century Brits pronounced the first vowel of Handel in a manner approximating a German ä. Indeed, the Great Vowel Shift that brought English language vowels closer to their modern equivalents had 1) already taken place by the 18th century, and 2) did not particularly impact the letter a as it appears in Handel’s name. I was tickled to find a video of an Original Pronunciation production of Shakespeare’s A Midsummer Night’s Dream on Youtube; it is delightful to hear the poetry rhyme. According to Linguist David Crystal’s pronunciation guide, even by Shakespeare’s time the ‘an’ sound had solidified to [æ] (think cat, bat, sat), as evidenced by the pronunciation of the words hands at 1:43 and can at 1:50. (But watch the whole video – it is a treat!)
A teacher of mine at Yale put it thusly, “The only people who are allowed to write Händel (or the standard varient Haendel) are the Germans; otherwise you’ll seem pretentious.” Even were one to make the argument that original names should be used for the sake of some standardized approach to cataloging historical figures, I rebut with six words: Sting’s real name is Gordon Sumner. The Encyclopedia of Popular Music (published by no less than Oxford University Press) lists Mr. Sumner under his stage name. Incidentally, The New Grove Dictionary of Music and Musicians (also Oxford Press) similarly lists Mr. Handel sans umlaut. The early music movement is obsessed with historical accuracy. Fortunately, the historical record is clear: George asked to be referred to as Handel. Who, indeed, are we to denationalize him?