Wife's Surname and Child's Surname - Whats the Islamic way?

I thought it was not possible to name your child like that only in the West? I mean dont you have to include husbands (or ur own - which is not islamically) last name as well?

Like for instance: Usman Khaliq has a son .. and they name him Idris .. so Full name would be Idris Khaliq, but you can include first name to so it will be Idris Usman Khaliq ? and not only Idris Usman, anyone?