How can I change the Account/Category on a Bank Register entry created by making a Bank Deposit & selecting a payment from Undeposited Funds. (It is greyed out.)

The entry in the Bank Account is probably correct.  That is the Acct you will see when you go to Banking and then Make a Deposit.

The proper Acct for the Items sold or Services would be in the Invoice you created and sent to your Client.  So Income:Consulting, etc. would be attached to the Line Items in that Invoice.

When you Receive a Payment, the amount is registered in the Undeposited Funds Acct.  This is a carry over from the days when people received a lot of Cash or Checks and had to go to the Bank.  Which they might do the next day or days later.  When you record the Deposit, you move the funds from the UDF Acct to the Bank Acct.

So go back and confirm that the Items in your Invoice are indeed set up correctly at that should show where the income from that Invoice was allocated to.

I was able to go back into the invoice and it looks like the category depends on the Product/Service selected? 

But in the bank register I still see "Undeposited Funds" in a greyed-out drop box. (Screenshot attached.)

After spending some time chatting with support, I realized that the income categorization is in the settings for the Products / Services on the invoice. (I also found out that our version of QB calls "Invoices", "Pledges".

I was worried it wasn't working because it wasn't showing up in the right category on the reports, but I discovered that when editing the Product / Service you have to check "Also update this account in historical transactions".