Can My Ex Change My Sons Last Name To The Guy She's With?

My ex (f24) told me (m29) that she will be changing our sons (m2.5) last name. She did not ask, she said it will happen and that she's just letting me know. She wants to change it to what ever her current boyfriends name is with his currentlast name hypened. So it would read" his name, midddle name, bio father last- stepfather last". But after they get married within the next year (she's only been with him since march) they are not engaged or married at this time. She wants to change it so he feels included in whatever family they make together and also because she said he will technically be her boyfriends first child.

I told her it is not an appropriate time for that topic nor do I think it's her choice or my choice to make, but our sons choice to make when he is older and understands what it means to change your name. She said it does not matter and it will happen regardless most likely next year.

Can she change his name without my agreement?

For context -We live in new hampshire -Never married -neither of us have sole custody, there is no parenting plan in place currently. So I technically can have him as long as I want without bringing him back to his mom if I wanted to be that way. -I am Currently on month 8 of trying to get shared custody -I am very active in my sons life and try to take him as much as I can