[Q] I want to root my phone but can't tell what model it is

Ok so I recently I got a phone off a friend, he said it was from Taiwan but I highly doubt that, and I want to root my phone, but before I do that I need to know what model it is. Under the model name for the phone info section it says "HTC-X710a" I tried searching it and multiple names have come up, HTC Raider 4G, HTC Vivid, HTC Velocity, from most to least common respectively. Is it possible to find the correct model name and carrier it was on using the serial number or imei number, or some other way?

Also, whenever using carrier-specific software to unlock the bootloader or whatever it is, is it asking for the original carrier or the carrier it is currently on?