Character ID info request

I am currently using a Non-steam client to try this out while i wait for funds to purchase via Steam. Started playing on my PC but when i tried copying the client data to my Laptop instead of logging into the same character (same name, same client data, same server) the server creates a new character with a duplicate name.

How does the Client/Server relation verify your character ID/name?

I know this isn't a "cheat" type post but i have a feeling i may need to modify the games files somehow to get my laptop to login to the correct character so i can play while out and about.

Let me know if I'm getting this right:

You want to know if it's possible to change a file to simulate you being on the same computer?
If it's a different Steam account, you'd have a different SteamID (hopefully you get that)... Now as for you just switching computers and not being on your original character? That's quite odd.

Oh wait, I just read and you said you're using Non-Steam... Please don't ask for help with a pirated game. Legitimate copies only. :L