Like you, I also enjoy the Annelise spelling; but Anneliese is more common in Anglophone countries (with Annalise being most common - despite the name itself not actually being that common - though I don't care for that spelling). So someone with the spelling Annelise would likely have it misspelled as Anneliese or Annalise quite a bit.
Analise looks like analyse / analyze, I don't like that spelling at all.
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