It seems that it's not a proper name, but a dialect word meaning "godmother".
(My mother tongue is German, but I never heard this word form, only the form "Gotte". Maybe "Gothel" fell out of use a long time ago, or is in use only in some regional dialects.)
I found this German text about the fairy tale that gives this meaning:http://www.gabriele-uhlmann.de/rapunzel3.htm
And this text confirms, in a context that has nothing to do with the fairy tale, that the word existed and really had this meaning:http://www.sagen.at/doku/volksleben/geburt_kindstaufe.html