Naming your child after...

So a little back story. My fiancé has a daughter from a previous relationship. We have a daughter together and are 4 months along with our son. Deciding on a name has been anything but easy. But to make matters worse my fiancé insists on naming him, which I’m not opposed to.... except for the fact that the only name suggestion he has is the boy name that him & his ex were going to choose had their daughter been a boy. She cut him out of his daughter life and took him off the birth certificate before everything was said & done in the hospital along with giving the baby her last name. They were in a committed relationship and not having any issues but she let her grandparents influence her decision. He constantly reaches out to ask about his daughter they share and now all the sudden that we have another baby on the way she’s trying to respond and give vague details. Their daughter has a medical condition that she’s unwilling to share any info on which has caused us to spend the extra money doing genetics testing with both pregnancies Incase the condition had been genetically from him. It would have been much easier had she been mature & just shared the information so we could explain to our doctor and so she had the knowledge of previous family conditions. I guess you can kinda say her pettiness in all of this is what’s really pushing me over the limit as to not wanting to even consider the name he wants because I’m constantly going to think of the bogus way she’s acted towards him.

Would you ever choose to name your child a name you knew your child’s father (or mother )was going to choose with their ex? Why or why not?