Greetings!
There is not, at present, a method to use parameters (such as the hostname) in the copy command within the switch CLI. (This can be done programmatically, however, using the built-in REST API in conjunction with a scripting language or automation platform.)
With regard to using protocols other than TFTP: ArubaOS-Switch also supports SFTP and SCP (the latter of which requires file transfers to be initiated from the management station rather than the switch). To enable these protocols from the CLI, enable SSH (if not already enabled) and run the following command:
switch(config)# ip ssh filetransfer
This will enable SFTP/SCP and disable TFTP. You would then use the following syntax to copy files from the switch to an SFTP server:
switch# copy startup-config sftp user@server