Bowser has only one son?

[Ridge Troopa]

That's typically the consensus, yes. If we assume adoption, though, Morton is named after his biological father.

There was some point in my gaming life where I thought that Mario ultimately killed him in SMB3 and now fights his son in SMW (because the game guide for SMB3 didn't include the Jr.).

Just like Mario killed the first Donkey Kong............ wait