Most polytheistic religions that don't have some sort of set pantheon of a handful of gods and no one else will have absolutely thousands or even hundreds of thousands of gods. For example the Greco-Roman Pantheons and Hindu ones.
I know some gods were taken over by Romans as they conquered land, but are there also cases where people make up gods? I mean, without trying to step on too many toes, they all were of course. But could you just make up a god in an afternoon and was it accepted that that was then an accepted god of the pantheon? Or was it necessary for a priest to be involved and somehow make note of the new deity for the "archives"? I suppose the best way to find out would be Hinduism, since that one's still around.
But could you just make up a god in an afternoon?
Yup! A lot of stories about Gods and Goddesses in Hinduism originated from local retellings of fables or epics, or just local interpretations of how certain canons went down.
There are a lot of branches and modes of worship within Hinduism too, so when you say Hinduism it really doesn't mean anything specific, just a blanket term. It could refer to Shaivism (Shiva worship), Vaishnavism (Vishnu worship), Jainism/Sikhism/Buddhism (their own religions now, but at one time all Hinduism technically) or a whole other variety of sub-religions.
For example, in the famous Ramayana epic, the demon king Ravana is canonically seen as the "bad guy" who is filled with malice after receiving a boon to never be killed by a God and then going on a bit of a power craze. However, in some parts of South India, they actually read the epic and see Ravana as a noble man who fell from grace, and his power is revered.
How certain Gods get added to the "pantheon" is just a local tradition picking up traction over time. I'd suggest reading more about the Puranas -- a set of ancient Hindu texts explaining a lot of personal stories about the Gods. Super interesting.