I think they are too similar, even though they don't actually rhyme in Finnish.I'm all for shorter name combos, so I'd stick with just two names.AnniinaLaurencomes to mind.
I actually prefer two name combos too, but I'm having hard time finding any nice combos with Anniina as first name.AnniinaLauren is something I've never thought of, but it actually sounds nice. Too bad it doesn't really work with the surname in question.