Yes, the owner makes a reservation In your name. Typically, the owner makes DME, but there are now reports that renters can just give them a call with the reservation number and set it up themselves. Or, use an online form to do it,
Once you have the reservation number, you enter it in to your own MDE. Just be sure, that before you enter into a rental, that you understand all the pros and cons,
You are renting from an owner and not Disney, The savings are great but typically cancelation is very restrictive and many times, not alowed,
Using a broker can also be a good thing as well. Be sure not to respond to any PMs you get and report to mods.