There is quite an extensive writeup on Bane in Dragon Magazine #372 starting on page 24:
As it notes, the writeup is mostly generic, rather than being specific to a setting:
BANE VS. BANE
The Bane of the core D&D® setting is not the same god as the Bane of the Forgotten Realms® setting! Oh, there’s substantial conceptual overlap. (The matching names probably clued you in on that.) They serve roughly the same purpose in the pantheons, their religious precepts have a great deal in common, and they make use of similar tactics and servitors.
Yet their differences are many as well, especially in terms of personal history, behavior, and even appearance. All that follows describes the core Bane, and it shouldn’t necessarily apply to the Bane of Faerun.
There is no specific lore in this article regarding the departure of a follower, however it does give some examples of Bane's displeasure:
Omens of Bane’s displeasure include the following:
♦ Weapons rust and tarnish regardless of how much care is lavished upon them.
♦ Long-healed wounds ache.
♦ The worshiper grows clumsy and drops weapons during practice.
♦ Warhorses, hounds, and other beasts of battle snarl at, and refuse to cooperate with, the individual.
Faiths and Pantheons (Forgotten Realms setting) suggests that leaving the fold would be punished harshly, but again, there is no specific action named:
Dogma: Serve no one but Bane. Fear him always and make others fear him even more than you do. The 'Black Hand' always strikes down those who stand against it in the end. Defy Bane and die - or in death find loyalty to him, for he shall compel it. Submit to the word of Bane as uttered by his ranking clergy, since true power can only be gained through service to him. Spread the dark fear of Bane. it is the doom of those who do not follow him to let power slip through their hands. Those who cross the Black Hand meet their dooms earlier and more harshly than those who worship other deities.
So while there is no specific penalty, the indications are that Bane and/or his representatives will make the PC's life miserable and preferably short.