I have always did it like this:

rcp filaname usernameinserver@server:path/in/server

The command will ask you for your password on the server (unless you are using another authentication schema).

Note that your user name in the local computer is not relevant.

rcp/scp are tunneled under ssh, it's probably the most secure way to copy a file. If you want increased security you can try to use key pars instead of passwords. It's more complicated to setup but after it's done you don't need to type your password for each transfer.