I would say use it however you like :) my little guy is gonna be named after his daddy but we are using the second instead of Jr. :)
Jr is really the father's excat name middle name if has one and last name. my boy will be named Joshua Tovar Jr. My boyfriend doesn't have a middle name. He is super excited to have a jr. His calling our boy his little him.
You can use the suffix at the end of a name after the father or you can use junior as as name.