Changing team name that appears in stats in CS:GO

Solution 1:

The team names are representative of the groups that you belong to on Steam.

In order to change the team name you must belong to any group that has a tag. You can find these groups under the Community section of your Steam Interface. Many public groups are open to join with little hassle. Simply click the join group link on the right hand side.

After you sign up to any of these groups you can change your settings in game to the tag you want. In game go to "Settings menu" → "Game Settings" → "Team" → "Steam Group Clan Tag":

Solution 2:

mp_teamname_1 and mp_teamname_2 in the console

optional: mp_teamlogo_1 and mp_teamlogo_2 i.e mp_teamlogo_1 vp (short for Virtus Pro)
mp_teamlogo_2 liq (short for Team Liquid) and mp_teamflag 1 and mp_teamflag_2)