Just for fun, I put in a long string of letters to see if I would hit a character limit for the fan name. But I didn't encounter a limit after holding down the g key for a minute. There has to be a limit to the amount of letters or words we can have on our badges.
Yes, it is currently 100 characters. The form is only validated when you submit it, not on the client side, so your web browser will probably allow most any length. You'll get an error after it's submitted about any problems like it being too long.
Note: The name will be compressed in the horizontal direction until it fits the badge label. It's hard to predict exactly when this becomes a problem, as some characters are wider than others ("i" vs "M" for example), but I doubt it will be a problem unless you go /really/ crazy with a long name.