Can you have a companion from your backstory?

My character’s backstory is that he had to flee his city because he used a spell to save his best friend in the city watch (a made-up city where spells and powerful magic were privileges that only nobility could have; it was illegal for commoners other than having simple magic items, like a broom that sweeps by itself). My character had been studying in secret and is a level 3 fighter with eldritch knight archetype.

Note: this is actually a replacement character in case my main one dies or if I play a campaign that starts at level 3.

Is there a way to establish that his best friend ran away with my character and become a companion or something? Or, does that have to stay in my backstory?

While I realize that some responses will be "ask your DM" I’m looking for (1) if there is a way to do this and (2) if you have experience in making this work.

This is my third D&D character so I’m still new-ish to the game and I’m not entirely sure if this is feasible and/or practical.