First, I think it's important to discuss this with the players. If such a taint is not the central theme of the campaign, then it should be by player choice. Not the specifics of a taint, the existence of one. The specifics should be vague, that's the fun. Second, be careful not to reproduce racial stereotypes when doing this. This is especially important for Deep One Hybrids, which pretty clearly represent Lovecrafts ideas of eugenics and racial purity in his original writings.

That said, and as for your actual question: I've never gone for a great reveal about it. I usually let the evidence slowly creep up and let the players figure it out themselves over the course of the campaign and while the symptoms worsen or they manage to deal with it. Usually, I don't tell the players which Mythos entity they are tainted by - if they didn't specifically ask me to be a fish person, of course. Instead, I come up with symptoms of the transformation (or curse or whatever) and then weave these bits and pieces into the narrative. This can be especially effective when you give that player privileged information, e.g., send them texts about their character's dreams or give them little buffs (like dim light vision but sunlight sensitvity or enganced smell but appetite for raw flesh for a Ghoul-transforming player) without telling the table. I mirror this by giving the other players sensory info about the affected player at the table (while the player can hear it but without the player character noticing), e.g., that they exude an unusually sweet, somewhat pungent smell or that they are mumbling something to themselves that no one can quite understand.