Forget about me for a moment and put yourself in my shoe, I am sure there are family men and women on here, what will you plan to do if you are in my shoes right now?
I am a family man too with a wife and three children, what I would tell you is, hustle, do all you can to give your child or children the best of life, a good life..
Whether you decide or choose to mine bitcoin in his name, or create a bitcoin wallet in his name and out in some bitcoin there every month doesn't really matter, remember that this is not the only child you will give birth to, you still have others coming, so better don't start what you are not sure of finishing..
This kids will eat and they need to eat good food, they will go to school, good schools in my country is very expensive, I don't know about that country you live in, they will wear good clothes, shoes, and so on, you have alot to spend money on, so hustle and make good money first, with time, you will realized there is alot to do for your son, or children, much more than mining bitcoin in their name or saving some bitcoin monthly in their name..
Anyway, congratulations bro and welcome to fatherhood..