A writ was placed on my bank account and the agency seized all the money in the account. If I open a new account in a different bank, does this agency have to go back to the court for a new judgement and how does a collection agency find out where you bank?

No the judgement stays active for 7 to 10 years normally

They will not need a new judgement. It is easy, they run either a credit check, or a check on a bank system to check for bad checks written. The collection people see it when they run a report on you

That is assume that the bank will open an account with you having a open judgement

They don't need to get a new judgement, but they will probably need to get a new writ. Most writs are written to only cover a specific bank, maybe even a specific account.