I just looked at my router and the number in the device name appears to be the phone's IMEI, and you can't change that. It's been a while since I've set up my phone but I can't recall ever giving it a device name nor can I find anything in settings to do so. Maybe there's an app or mod that will allow the phone to broadcast a different device id. I don't know the technical aspects of that.
Makes me wonder though. Is there any security vulnerabilities having your IMEI available like that? Say if you're connected to a public network and someone can view the DHCP client table, is there anything nefarious they can do if they have your IMEI?