Eloïs or Eloïse

I find Eloïse a bit more common and clearer. That's why I vote for it.
Here are some more options: Loïs Lois Noï Loïse Louisa Elora Elenor Eleonor Elodie Estelle Estee Luce Elize Elice Lise Ise Isaï

Eloïse is just prettier, Eva. It sounds softer and calmer than Eloïs. I do know people with the longer version, and they often find it a much nicer spelling. The stress also falls just a bit differently. When it comes to the sound, Eloïse wins.