If you give someone the name of your accountant and name on the account do they get access to your account? Accountant like the person helping you manage your money. I have someone offering to make a deposit in my account but all they need is my bank, my accountant and the name on my account. Is this a scam? If I give him this information can he access my account? He didn't want to use square cash or Zelle. Should I be worried?
Yes, you should be worried.
Technically (as per Nathan Merrill's answer) the information they are asking for is not enough to gain access to your money. However, either you or they have mis-used the term accountant which does not mean a person in a bank who manages your account - an accountant is a professional who helps an individual or company record and report their finances for tax returns or company financial reporting. More likely they are trying to get your account number, which they would need to make a deposit (and would also allow them to potentially gain access to your money).
Long story short, if someone needs your bank details to make a deposit (especially if you haven't met them, or they contacted you out of the blue, even if they spin a good story about why they want to make a deposit) and refuses to consider any other means of paying you, then they are trying to scam you in one way or another and it doesn't matter what the details are: you should cease corresponding with them, block them, delete any messages, and move on.
With just your accountant's name, no.
It's possible that the name of your accountant could assist as they try to social engineer into your bank account, but banks have regulated processes and the chances of that working are very low.
Barring that, the name of the accountant does not reduce the security of your bank account: they will need other information (a password, or an account number, etc)