Yes, and here's how:

When you get to the ENTER CHAT page you type your agreed private room name into the NEW ROOM text box, and click the button for Private that is nearby.

If 2 people enter the same name, they both get there.

One person is creating it and one is joining it-- using the one-and- only box open to try it. When I had an invite in the past, I didn't realize that text box is not only used in creating the room but also to get in if it has already probably been opened by your chat-bud.

Also I was delighted to find in my prior pet chat that I could copy all the text, and dump it into email for further clarification.

Thansk, Bill!

~Susan