I actually was enrolled into "My Hyatt Concierge" in June with this email:

"Welcome to My Hyatt Concierge, a benefit of your World of Hyatt
membership..."

I was given an email address and phone number to contact regarding:

"I'm here to help make your travel planning easier by booking and
customizing your Hyatt stays and keeping informed about our latest
promotions."

I'm not sure how many nights I'd had at the time, but probably over 80. I've never had a private line rep before.