Yeah, I don't think English rules are consistent enough either way with -ise and -ice tbh. =P We have Beatrice, and we have Bernice. We have Janice, and we have Patrice. Lots of examples from words too - police vs office vs sacrifice, etc.
But I know what you're saying - most -ise names end in EES, and I agree that I would think of Elise first. I was surprised when I searched for the name and saw it as a variant of Alice.
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"We are all horrible and wonderful and figuring it out." - Harris Wittels