I have free electricity via solar power with enough juice wasting everyday, maybe I should start mining some BTC in my sons name for his future.
This will not be as easy as you think, maybe the second option below could be better.
Maybe I should just get a wallet in his name and start buying small piece on BTC for him every month.
This is an easy way going method and I encourage you to do that. This is what all bitcoiners are supposed to do.
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?
It's your bitcoin, it's your baby, do what you like. If your baby grows, he could change anything they don't need.