Tap on your profile picture on the top left side of the screen. By default this will open up the “Player Level Rewards” screen. From here just select the tab next to the current one at the top of the screen. This will be your profile tab. On this screen, simply click the pencil icon in the square and this will open up the name changing screen.
To change your name in COD Mobile you need a name change card
On this screen you will see the option to input a new name and what the cost is. Unfortunately, there are a couple of costs associated with changing your name. The first is that you can only change your name once every three days. The second is that you need a Name Change Card to do this and a screen will pop up that notifies you of this.
We haven’t seen name change cards in any rewards in COD Mobile so it appears that the only way to get a name change card is to purchase them with COD Points. The price of a name change card is 500 COD Points.
Once you’ve got the name change card you will see your name change effectively immediately after you’ve spent the points.