Then they will either return to their original location (except for Raul) or can be told to go to the Lucky 38. If the player already has a companion of a specific type, they need to be dismissed through dialogue.
Companions are controlled via the Companion wheel. From left to right: Rex, Rose of Sharon Cassidy, Raul (Vaquero outfit), Lily, Boone (assault armor), ED-E, Veronica, and Arcade.
All eight permanent companions in Fallout: New Vegas.