Kinda. There’s a fast way and a slow way.

Fast way: You have to dock with the enemy ship, clear it, sit in the seat, undock from your main ship, quickly open the menu, set the ship you’re in as your home ship, redock with your main ship before it flys away, and then presumably you’ll want to set that back as your home ship.

Slow way, dock, clear, sit, fly somewhere (grav jumping sets whatever ship you’re in as your home ship), land at a ship technician, set your main ship back as your home ship. You have to repeat this for every ship you take.

The fast way keeps you in system with your main ship so I prefer it, especially if I’m in the Serpentis system trying to make 100,000 credits collecting var’uun ships.