The source of their power can vary. Regardless, it is canon that Paladins don't strictly need deities these days. I'd recommend having a read of the entry from the player's handbook.
Gods feature frequently and often in Paladin stories, but it is only a 'Many do' situation now; their power comes from their commitment and their dedication to an oath or cause, or to their vision of righteousness. Deities need not be involved any more. Their power is a divine power, certainly, but in many cases it is pure divine force, not tethered to or channeled through a particular deity.
I’d argue it depends upon the world setting. In Eberron, the gods are almost abstract concepts. So paladins don’t need a clear divine source.
Forgotten Realms, the gods are very much real and do provide divine powers. I don’t see how a paladin in FR could have powers without a god providing their powers.
