second baby!

Melissa
Question?? If I have a boy from a previous relationship who has no ones name in particular is it ok for our second child to have my SO first name? Wouldn't it be hurtful for my first child? This is so stressing me out because I love my child and I don't want to make him feel inferior or something. At the same time I also love my SO because he's been such a great dad to my first child and I know it will mean a lot to him to pass on his name just like his dad and his grandfather... 
Edit: my son is not my SO biological son. He comes from a previous relationship.