Baby last names

So me and my boyfriend are expecting our first. We are not married not sure if we ever will. He has two last names (his moms and dads) and wants to give our son both his last names and mine at the end. That means our son would have 3 last names so 5 names total. It seems like too much to me. He said we can drop my last name. What would you do? Can me and my son having different last names be an issue? I have a daughter from a previous relationship and her last name is my last name-her dads last name. My current bf wants his last names first and either drop mine or put it last. I’m not sure what to do.