If you're using a traditional name, I recommend using one of the widely accepted spellings. In other words, I'd go with Elisabeth or Elizabeth, but I wouldn't try something bizarre like "Illyzubith." Bending over backwards to use a spelling like that just seems a little too pretentious. On the other hand, if you're using a very nontraditional name, or a name of your own invention, then there really aren't any accepted spellings. If you go this route, do remember that your mother has a point about having to spell your name every time you give it. The same applies if you use a weird spelling for a traditional name--the person will have to spell it--and correct the frequent misspelling of it--his or her whole life.