Well I don't know if it's best or not. But you said you wanted:
to copy the database from one server to another, work in another server, and re-copy it in the original server.
(and additionally end up with the database having the same name on the original server.)
So your steps do seem like they would be one way to accomplish that. What counts as the "best" way would depend on what else is important to you about this process, i.e. what criteria would you use for best?