Hi Jeff,
Sorry to hear about the tension in your little one's life right now.
I have to weigh in with the posters who are of the opinion that the name is relatively unimportant.
Having said that. . .
What is important is your relationship with K. Now, some of that for you, and for him, may indeed be tied up in naming, but I would be concerned that this not turn into a struggle with your Ex. that escalates to the point of her further attempting to alienate you. Your description leads me to believe that she is either less than rational or vindictive. Giving her the benefit of the doubt, and only going by your account, I'll presume the former.
You've described her paramour as being disinterested in his own two children from a previous marriage. If that is indeed the case, I highly doubt that he is particularly interested in your son except perhaps as a means of furthering his relationship with the Ex, or antagonizing you--again to the benefit of his relationship with her. I suspect that this whole name thing is her issue and that she imagines he might have more of an emotional investment in K. if he's called something different. Has the fiance said anything to you about this, or is this all coming from Ex.?
A few more thoughts:
This is likely to get worse before it gets better and as hard as it is try to resist the impulse to antagonize her.
My husband has a friend who was divorced when his daughter was 2. Although his Ex. was less than ideal, she got custody (this was many years ago) and he had to grin-and-bear-it for 10 years, until daughter was old enough to have her request for custody considered by the judge. At 12 or 13 she finally was able to live with him. . . happily ever after.
He did a lot of really clever things all those years to make his presence continually felt in a way that Ex. couldn't prevent.
He kept a current picture of his daughter next to his bed (it went with him when he had to travel) and first thing in the morning he talked to her, told her he loved her & missed her and would soon be with her. Same thing last thing at night. The important part was that he let her know this so she could picture him doing this every day. After a bad day, and no matter what was happening with her mother she knew he was loving & missing her.
He called every day to talk to her even if just briefly. I think there was something, too, about ringing once and hanging up, but I don't remember the details.
He collected pennies for her, too. Any penny he picked up or got in change he thought of her and kept in a glass jar. She collected pennies too. When she was with him they'd count and roll them all and he'd sneak a few into her things for her to find when she went back to her mother. I never asked her, but I'm sure that everytime she picked up a penny she thought of him--I'd expect that she still does to this day! I don't think the Ex. knew about the secret pennies and what they meant to the two of them or she would have intervened. Otherwise a child who insists on picking up change and saving pennies seems pretty innocuous.
He was a great father and he truly did what was best for his child, hard as it must have been. He managed to "be there" for her every day in a way, and I think he managed to do it without it being about him and his needs/wants, which she really needed. Her mother was really quite unstable and needy--not acting in daughter's best interests--and thwarted him whenever possible but he just kept on and took it, and it all turned out well in the end.
Choose your battles wisely and remember that what really matters is your continued relationship with your child and how he will come out of this in the long run.
Teresa
p.s. More visitation is excellent. Maybe he could stay with you while she recuperates from her knee surgery. Make the offer to her fiance! ("Al, I'd be happy to have K. with me while Ex. is recovering from her surgery. I know you will really be needed to take care of her. . .)