I honestly think that you should be able to buy companions like Ensign Emmett or Lucky Jack Russell from the crowns shop with their respected name and "personality". I like Lucky Jack Russell so much and I wanted him SOOO much, but I couldn't get him anywhere. I was losing my mind I wanted him so bad, but I was really disappointed to find out that you can only get him if you chose "Shipwrecked" and I was just sooo sad, and I wanted to start ANOTHER new character just for him, but I got so far on my first and second character that I didn't want to stop playing as them, but I was still losing my mind. I think the companions in the crown shop that's like them should have their respective names and it should be that you promote them like normal. At least it should be that when you create a new character, it TELLS you what companions you get (at most: the starting, the treasure hunters, and the Presigio) because I was (and still am) losing my mind for Lucky Jack Russell.
Please consider this. I'd be more at peace and ease to actually get Lucky Jack Russell, even if he is from the crowns shop, but a lot of other people like to see respective names put into the crowns shop. I've asked some of my friends, too. They agree with me.
I actually like the fact that the Crowns Shop Companion are different in appearance and name. I enjoy having "Sergeant Shepherd" on my Crew instead of Russell. I like how he is named after the NPC we meet in the first Main Quest in Skull Island.
Besides, I've seen screenshots of people who obtained Lucky Jack from the Presidio and purchased Sergeant Shepherd. (I myself have Gaspard and Giordano, and Emmet and Exeter) Would be kind of trollish to transform the Crowns Companions into the regular ones if that means you'll have more than one copy!