Interesting.
I am not German, but I've been living in Germany for years now.
I actually know a guy called Händel. He's a friend of a friend, and I've met him several times at parties etc. When I found out what his last name was, I was ecstatic (and he was perplexed...).
So I hope the OP understands when I write Händel. Händel himself anglicized his last name, understandably, so it's obviously ok if people write Handel.
Also, Handel is German for "trade" or "commerce", and it would be pronounced quite differently (/'handl/ instead of /hɛndl/ in a phonetical transcription using the International Phonetic Alphabet), which makes it all the more weird for German speakers to use the version without umlaut.
There's another point I believe is relevant to this discussion, and that I've never seen raised. These days, the English pronunciation of Handel and the German pronunciation of Händel are different (/'hændl/ vs /'hɛndl/) but, and here's the interesting bit, they were identical in Händel's time. Back then, the English would have pronounced Handel the way the New Zealanders would pronounce it these days: that is, the exact same way the Germans pronounce (and pronounced) Händel (/'hɛndl/).
British English underwent a vowel shift in the mid-twentieth century that saw the pronunciation of those a's (as in "cab", "back", "bat") move from /ɛ/ to /æ/. The shift is so recent that it can be observed in the same person: Queen Elizabeth II can be heard using the old pronuncation in early speeches, but she uses the modern one now for the same words.
University paper about this:
http://phonetik.uni-muenchen.de/~jmh/research/papers/harrington00.jipa.pdf
Telegraph article:
http://www.telegraph.co.uk/news/ukn...ueens_diamond_jubilee/9280753/The-Queens-English-changes-through-the-years.html
Incidentally, this phenomenon can also be heard in the accent of Stewie, the baby of the TV show Family Guy. The show creator and dub actor, Seth McFarlane, once said he took Stewie's overly affected accent from Rex Harrison, the British actor who desperately tried to teach Audrey Hepburn how to speak proper high-class English in the film My Fair Lady.
You will forgive me for this rant, but I'm a Händel hooligan and a linguist, and well...