Well....
2e DMG ...
"It is common to find the paladin working in association with the clergy of his religion, but lone paladins, carrying their faith into the wildemess, also appear in the tales of bards." p. 18
"One important, and potentially life-saving combat ability available to priests and paladins is the ability to tum undead. This is a special power granted by the character's deity. Through the priest or paladin, the deity manifests a portion of its power, terrifying evil, undead creatures or blasting them right out of existence." p. 67
(See also, evil priests turning Paladins, p. 68)
From the PHB- the Paladin acquires and casts spells, and must abide by the rules for the Priest in doing so- under Priest, it states that the Priest can cast spells "primarily to further their god's aims[.]"
All excess money must be donated to "the church" (note- not a church, or a religious institution ... THE church).
The point of this isn't to be pedantic, BTW. There is always a huge difference between the game as written, and as played- perhaps moreso when looking back. There was a lot more murderhoboing going on than, um, careful attention to whether or not you were advancing St. Cuthbert's aims. But I would say two things regarding the game as played, regardless of the rules:
Most Paladins, were followers of one god. It was kind of sort of assumed, for the most part. IIRC, the character sheets had a space for deity, not deities.
Most tables, and most players, didn't do a whole lot with the deity thing. Unless it helped you kill MOAR ORCS!