Name and IL problems

My FIL insists on misspelling my newborn’s name. I have corrected him a couple of times, but he keeps using the spelling that he believes is the right way to spell her name. If I try to correct him, he will launch into an long argument on why his way of spelling her name is the right way (it’s one of the ways, it’s not THE ONLY way) And I’m like it doesn’t matter, her parents named her, so that’s the spelling until and unless she decides otherwise! We live far away, so it’s happening a lot on texts.

I know in the grand scheme of things, this is tiny and inconsequential - but it irks me to see him refer to her while misspelling it nevertheless.

Any of you fine parents have ideas on how better I can handle this situation/my feelings?