Where to enter 1099-INT PAYER'S Federal ID from the IRS on tax return?

Just put IRS. 

In the bank or brokerage name? So no need to enter their Payer Federal ID number?

You shouldn't need to enter an EIN.  Just enter a name like US Treasury or IRS.

The IRS took so long last year to pay refunds they paid interest on it.

Enter interest from the IRS like a 1099Int and put the amount in box 1.  Enter it manually and just enter IRS for the payer.  Don't enter any other info like the address or a EIN.

Enter a 1099-Int  under

Federal on left

Wages & Income at top

Interest and Dividends

Interest on 1099INT - Click the Start or Revisit button

Don't enter a bank or broker name and don't try to import it.  At the bottom pick -  Change How I enter my Form

Then on the next screen pick I'll Type it in Myself

I'm using H&R Block and there is no "Payer" box, only "Bank or brokerage name". Can I put IRS in the Bank or brokerage name?

Yes, enter IRS for the Payer of the interest in the spot for the Bank or brokerage name.

This is only the Turbo Tax forum.  We can't answer for HR Block. They probably have their own forum.