This is very well done in Dimension 20's Fantasy High live-play games. One of their dieties hates part of itself because they have 2 different worship bases, and one base REALLY hates the other base and ended up nearly wiping out the original worshipers. This has resulted in the god having the personality worshiped by the second base, with traces of the first personality still coming through, and hating itself for when that happens.
Something like would probably require the Gods to be very active in the world, just to protect themselves, since it enables the option of a hostile takeover or pseudo-mind-control of a greater power. With how easily cults are formed here, a world where the Gods are demonstrably real and mind control actually exists would just make it that much easier to create offshoots and true believers.