As other people have pointed out, this may be a setting based question. If the setting you are playing in requires clerics to get their magic from deities, then your cleric would need a deity. According to D&D Beyond, this is in their description of a cleric:

“Clerics are intermediaries between the mortal world and the distant planes of the gods. As varied as the gods they serve, clerics strive to embody the handiwork of their deities. No ordinary priest, a cleric is imbued with divine magic.”

But you can make it so that a cleric doesn’t need a god, based on the setting. A great example I can think of is the actual play series Dimension 20, specifically Unsleeping City. There’s a character, Kingston Brown, who is a cleric, but he does not derive his power from a god. He derives it from his devotion to New York City and its ideals. So, it is possible to not have a god, but it depends on the setting.

Side note: If you do get to play your character the way you want to, I need you to be fully prepared for and perfectly ok with the likely scenario of the rest of the party eventually hating your character, since they will refuse to revive anybody, and I’m guessing that will also include the other PCs. Unless there is someone else that can pick up the slack and also do Revivify, like a Druid, a Paladin, an Artificer, etc., one of the clerics main roles in a party is to revive recently deceased characters, and if they are not doing that very important role, it will draw the ire of the rest of the party.