When you purchase a gun from a gun dealer is it also registered at that time?

Depends on where you are. In MOST of the US, there is no requirement for registration of common firearms. The dealer must maintain a record of sales, but there is no "registration" per se.
Depends on where you are. In MOST of the US, there is no requirement for registration of common firearms. The dealer must maintain a record of sales, but there is no "registration" per se.