I first encountered the name [name_f]Catriona[/name_f] in a book as a young teenager, and thought it was pronounced as it was spelled: [name_f]Cat[/name_f]-ree-oh-na. When I learned that it was actually pronounced [name_f]Cat[/name_f]-ree-nah, I was dismayed. Not because I had been wrong, but because I really liked my original pronunciation as a unique name (I was reading a fantasy novel set in a made-up place, so I was quite prepared to accept any and all names as made up but close to reality; there were many names in that series which I thought were invented, only to find out they weren’t). Anyway, [name_f]Cat[/name_f]-ree-nah, to me, was spelled [name_f]Katrina[/name_f]. So for me, even now, [name_f]Cat[/name_f]-ree-oh-na has a sort of magical and romantic sound.
That being said, I would stick with pronouncing a name as the actual pronunciation dictates. I am a fan of being and sounding educated.
On the other hand, I would consider playing around with spelling to see if I could come up with a spelling to match the pronunciation I wanted. I’m not sure I could find one I’d be pleased with, though.
Also, truthfully, the spelling [name_f]Catriona[/name_f] is so unusual here in the States that I’d seriously consider using whatever pronunciation I wanted for it. If a British kid can be named [name_u]Brooklyn[/name_u] or [name_u]Cruz[/name_u] or [name_m]Romeo[/name_m], without any personal family ties to [name_m]New[/name_m] [name_m]York[/name_m] or [name_f]Italy[/name_f] or the Spanish language, and if girls can be named [name_u]Ryan[/name_u] and any child can be named [name_u]River[/name_u], I’d say [name_f]Cat[/name_f]-ree-oh-na spelled [name_f]Catriona[/name_f] is totally and completely a viable choice. A kid with a story about their name in this day and age, especially one in which the choice was deliberate and not a mistake (as opposed to my HS teacher, years ago, whose friend was named Janith because her dad had a lisp and the nurse wrote it down that way), is totally fine.
Edited to add: I wrote my post before I’d read all 4 pages of comments, and I have to say now, after reading about other pronunciations, etc., GO FOR IT. It’s a legit pronunciation, anyway. I wouldn’t change the spelling or anything, except maybe including the diacritic you mentioned. But if your main concern is “being correct” I’d probably leave the diacritic out if it’s not original to the spelling. This is a head-vs-heart decision: you like it but you think it’s wrong.
Well, it’s not actually wrong, so there’s no actual debate, here, after all.