Coincidentally, I called Equifax and talked to someone yesterday. I asked my question and got it answered: If I just give my name change to all my creditors, the credit reporting agencies will get that information. I don't need to notify the credit reporting agencies directly.
Here's how I got to have this conversation: My wallet was apparently stolen the other day. When I made a police report, the cop advised me to contact the credit reporting agencies and make a fraud alert (to prevent identity theft). I got the number for Equifax and called, and using the touch tones entered my information and did this automatically. After that I stayed on the line and a woman spoke with me, she tried to sell me some extra credit protection, I politely declined to buy, but did get that answer out of her.
The timing to have my wallet lost or stolen was perfect. All the ID and cards in it had just become obsolete since I have notified everyone of my name change, and all are in the process of being replaced. So if anyone attempts identity theft, my old data will be no longer valid anyway, hee hee.
Kate, that's interesting you and I are going through this process simultaneously.