To transfer an alias which you own to another user you must first get the full public key of the user’s address you which to transfer the alias to.
The recipient can get their public key by navigating to the “Aliases” tab and clicking “New Public Key”. They will need to send you this key so that you can transfer the alias to them.
Once you have the recipient’s public navigate to the “Aliases” tab in your wallet and right click on the Alias you wish to transfer. Select “Transfer” from the menu. In the dialog that appears enter/paste the recipient’s public key and click “Ok” to complete the transfer.