Arthur Carrington
You can escort arthur carington from vault 27 to phoneix wait a few days and talk to him.. he becomes a permanent companion ( if you don't let him go in casa nueva he's yours)
Paladin Barkley
in inferno sewers.. requires a 90% speech check in order for him to run with extra companions and he'll probably only work with you if you're with BoS, but otherwise he's permanent
Diana
Follower of Apocalypse in inferno after you finish the quest for the mutant leader there (and it's woth at least for the Power Armor), you can escort DIana to Casa Nueva, but you don't nessecarily have t release her there so in this regard she's peranent companion.
Senior Asistante
a Mr.Handy robot at you ancestor's toomb, that grany adonisa directs you after you finish the main quest and have the continue after MQ perk.
Eugene...
If you want to be really cheesy you can aquire the get an engineer for the dam quest before destroying the dam, destroy the dam, do the DLC and return, ad after that you can go grab eugene for that now unfinishable quest, so that he stays with you until he dies.. there's no way of disbnding him, and he's not scripted as a proper companion.. He's probably best with grenades, as he has no weapon animations, so it's only unarmed and no animation thrown weapons for him ( so no knives and no spears for throwing), he can wear armor for adults, but he looses all benefits of it after switching maps.