I was approached on Instagram by a painter who wants to use one of my posts as a reference for a painting for a client of his. He said my cut would be $500 and he needs my full name, and bank name for the check, along with my email. I asked if he could just Venmo or cash app me and he said no because his client has had problems with those apps in the past. So I’m a little sketched out. Not sure if someone can hack you knowing those 3 things.
This is a common scam on Instagram right now. You can find other examples on reddit of this; one example: https://www.reddit.com/r/Scams/comments/tbbpq6/artist_scam/
It's a fake payment scam. The words "your cut" (plus cheque payment) really give away their plan. They will send you a cheque for "your cut", plus supplies and payment to the artist, or something similar that you are supposed to forward on to someone else.
Then the cheque bounces awhile later, and all the money you forwarded will be gone (they will use an irreversible method), and you will owe the bank back for everything you forwarded.
The money from the cheque will show up in your account at first, and they will try to say that means the money is clear. The money is not yours. The cheque is stolen/forged and the transaction will eventually be reversed when the bank notices.
Even if they can’t hack you with just that information, scams can be elaborate and involve multiple stages of gathering information about you. The first part of the scam might be to obtain the name of your bank. Then they email you and say they’re from that bank and need something urgently. Then they steal from you.
I have written a few checks lately, and I did not need the name of the bank where it would be deposited. That does not sound like important information for writing a check. This guide makes no mention of the receiving bank, for instance.
To answer the question in the headline: you give people your name (not necessarily full name), bank, and bank account number every time you write a check. You give them your email address (not necessarily your primary address) every time you communicate by email. So those are nearly public knowledge, and there is very little damage that can be done with only those three. You do want to be cautious as requests for personal data go beyond those, however.
But the rest of the transaction screams scam. Nobody will ever legitimately ask you to open an account on their behalf, or run their money through your account, or pay a fee in order to receive a payment, or... Ask yourself why they need someone else to do whatever it is; ask why they need you to do whatever it is. If in any doubt, run away.