I don't think there is anything wrong with it. I have a cousin who's daughter has two middle names and both her first & last names are Arabic (last name is a compound name) so it doesn't get much longer or more complicated.lol Also, a member od dh's family named her daughter with a hyphenated first name AND a hyphenated last name so that is really five words to make 3 names. Basically, I think anything goes. If you like it and are fine with it--do it. She'll either love it or hate it.
