Unlocking and unbranding are 2 different things.
Unlocking - You can use any sim card once your phone is unlocked. The unlock code is provided by your operator as well as external parties, depends on who is your operator. (The free method) Chat with your carrier and tell them you are going abroad and need to use the same phone abroad and would like the unlock code, be polite and ask for supervisor if needed. If you have a good credit standing, they may give you easily else they may not, ultimately its their decision. Alternatively you can shell out a few quid and buy one from ebay.
Unbranding - You remove the Operating System installed on the phone by your carrier and flash/install a generic one, voids your warranty if carrier gave any.