Bajoran name system ran a little differently didn't it? Nerys Kira is how we'd present her forename and surname but there were cultural reasons for the switch. Am I remembering this right?
I just think the Abramsverse wants to play fast and loose with some of established pieces. Hoping that splintering off at Kirk's 2233 birth would be enough to do it with 100% freedom, but some of the reasoning has to worked hard to try and fit it in with what their nature is, in any universe... even a twisted evil one like the Mirror one. Sooner or later, I'm beginning to think they're going to undermine their own rule about everything up until the start of the film, being the Prime universe.
It comes across as somebody having thought "Wouldn't it be cool if Mudd had been a female Bajoran?" because the vocal Niners will get a kick out of that. Not a whole lot of thinking beyond that as far as I can see. I very much hope I'm proved wrong and there are well-versed fans behind this with an answer for everything.
Anyway what happened to Mudd's nagging other half? The one he had a robot version made of once? Stellaaaaaaaaaa!