Will my old teammate find me after I change my name?

Probably. Give them a bush. They should be able to figure it out, when they visit your island.

Also, if you two are FB friends, they will still recognize your FB profile picture, as long as you select the option to show your FB picture instead of your game avatar. To do this, tap on your picture, the pencil next to the picture, and then the FB image box. Only your FB friends will see your FB picture; others will continue to see the game avatar you chose.