Need honest opinions!

CeeTee • Mom. Wife. 25. 🐞Harper 4•25•17🐞 🐝Ava-Cate 9•24•19🐝
Should a child call their mothers boyfriend daddy? 
My husband has always been in our stepsons life, since the day he was born. He's six now. I've known my stepson for three years. We never ever made him feel like he had to call me mommy (because I'm not his mom) he is comfortable calling me by my name. That's perfectly fine with me. 
My husband's ex just moved in with some guy. They've known each other maybe 6 months. My stepson told us he is to call this man daddy. My husband almost cried at that because he is is daddy and has raised him from birth. Now his ex has two other kids who's father is not around, so I can kinda see them calling him daddy, but not my stepson. As he has a father who is in the picture constantly.  She is not married to this man.  Side note: my stepson has had a lot of men come into his life that she has termed "daddy John Doe" 
I'm currently pregnant and wonder if it's a way for her to hurt my husband because she wants full attention. 
Is my husband wrong for being heartbroken about this?
 To me it just seems very strange of her to ask my stepson to call him daddy, when he has a daddy.