Caleb had no idea where to go next. He couldn't go back to the temple. Master Obi Wan gave orders to remain hidden. He couldn't stay on Kaller. The Clones were still looking for him. Even if Janus and Kleeve were there to protect him.
Caleb just sat there in the escape trying to decide where to go and what to call himself. His life as the Jedi Caleb Dume was over. It had died with Master Depa Billaba. The Jedi had died with the republic leaving little behind. Nothing left but memories that would soon be forgotten by most.
The idea that the Galaxy could ever forget the Jedi was a little hard to swallow for anyone, especially a Jedi Padawan like himself. Caleb couldn't let that happen. Surely there was some way he could help keep the Jedi in the Galaxy.
That's when he remembered his master sitting in on a council meeting via holoimage the night the Galaxy changed. They had gotten an assignment to protect a newborn Youngling on Lothal. The Youngling was going to be force sensitive.
He could go there and find the Youngling and do as he and his master were supposed to do. Find the Youngling and protect him.
Caleb set the cordons of the ship for Lothal. He picked out his new name. He planned on telling the parents of the Youngling his real name and what he was, but no one else. He was now Kanan Jarrus to the Galaxy.
(Just run with it)