In my State (MT) an employer is issued a State ID for purposes of the Department of Revenue and the State Worker Comp Insurance. Notice the "WTH" is the withholding account. From the website:

"To get one, you'll first need to get a federal tax ID number. Once you have that, you'll need to apply for a Montana state tax ID number using either a traditional method, like applying over the phone, via mail, or via fax, or by applying online."

The Form uses the FEIN. Then the business is issued the ID.

https://mtrevenue.gov/wp-content/uploads/dlm_uploads/2024/01/Business_Registration_form_genreg.pdf

As long as the Entity that is registered with the State is the legal name, it's a cross-reference. You might confirm they did it right, of course. Due diligence.

I've seen where an old FEIN was still in use, or the wrong LLC FEIN was used for payroll, because someone thought it had to match the bank account, not the business.