Yes, but giving the baby his name is not going to actually do either of those things.
What will show him you value him as a parent and encourage him to be a responsible father are things like trusting him to care for the baby alone rather than micromanaging him and telling him how he should be doing it; sharing the load; discussing things about the baby together; seeking each other's opinion, listening and compromising where you have differing opinions.
The are the important things.
If you think about it, you've done the hard work for 9 months, you'll be going through labour, you'll likely he doing the majority of the baby related grunt work.
So why does he get to have the privilege of the baby being named after him but you don't?
You don't want to upset him and his family but where are your feelings valued in this?
And, put bluntly, if you and he split up, you will likely be the primary carer.
If he wants the baby to have his last name, he needs to show commitment (ie marriage).
It's not a gift for you to bestow upon him.