Step parents name vs biological parent's wishes?

To be honest, I'm doing this to hopefully feel better about my decision. My son is almost 5 & I've been with my fiance since he was 2. I tried to do 50/50 custody, but his dad gave that up &, even recently, said he can only be with him every other weekend. He's even admitted to wanting to send him back to me early bc he would constantly ask for me or get upset and only want me. Anyways, my son started calling my fiance daddy a few months after they met. My fiance helps me equally in caring for my son, including attending speech therapy sessions & picking him up from school. Recently, my ex had started getting upset that he calls my fiance daddy (I'm not sure if he just realized this was happening or not). Now he wants me to talk to my son and tell him not to call him that. I told him that it's our son's decision and if he changes his mind on who gets called what, it's his decision. Now my ex is mad saying it's inappropriate for him to call my fiance daddy.

So what do y'all believe step parents should be called? Does it depend on the situation & the family?