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This is actually very similar to a situation in my world.

One of the gods, Gol, is actually the remains of an evil elf king (there's been a few of those in my world) named Tembyrlane. He is evil through and through but heads a Neutral Good religion with the domains of things Healing, Magic and Protection. How does he pull this off? By proxy & manipulation. Gods in my world have "vestiges" that are portions of their power given sentience and autonomy so that they can act in the material world in the stead of the god since gods become more vulnerable when they manifest in the prime material.

It is important to remember that the concept that a god is "all powerful" is immediately false in a D&D setting because there are MANY gods. None of them can be all-powerful or all-knowing.

Gol, being evil, has created vestiges for himself that are Evil but that are also Neutral in alignment. Gol portrays himself as aloof and distant, telling people to work "towards" him. His vestiges act directly in the world and are portrayed as "voices" for Gol hence their neutrality (the neutral ones speak to his religious folks, not the evil ones) which does not seem weird to the worshippers because the "voices" are supposed to be impartial and unbiased...they act as messengers. So on one side you have an evil god, in between neutral messengers and good followers. Gol also impart spells to some of his clergy that allow them to make their alignment appear to be "Neutral" under the pretenses that this is to be done as a reminder that no being is "Good" until they are one with Gol and that they should not feel hubris about being filled with positive energy. Of course, this also allows those greedy, evil parts of Gol's clergy to continue operating under the guise of being "Neutral" as well and no one is the wiser (though to be fair, Gol's clergy is 99.99% unaware of the gods nature).

The way my world works, gods gain power in the afterlife by the energy of souls moving into their "realm"..basically their own corner of the afterlife. So if you die pledged to a god you get to go to that gods version of the afterlife before being recycled back into the material world after a time. so it benefits gods to have religions that attract people. The only exception is sacrifice...if you are sacrificed in the name of a god you are sent to that gods realm in the afterlife instead of that of the god you worshipped. This is one of the big reasons evil gods want their followers to sacrifice powerful souls to them. Gods are aware of how the afterlife works and, being a sneaky jerk, Gol uses this to his advantage. Many of his evil vestiges manifest in other parts of the world to start cults and such devoted to "new" gods (the vestige essentially). These cults typically rise in power and then clash with the followers of Gol and, when the time is right, the cults power is cut off (since Gol ultimately controls it) and the cult is crushed there-by proving the superiority of Gol...which leads to Gol getting more followers...and BONUS those cultists that were devoted to the false god and were killed ALSO go to Gol because they were, after all, actually worshipping a vestige of him. Win Win!

Hope that gives you some ideas about running an Evil "Good" god