That is correct no telephone # is needed for the receiving party - nor does the receiver need to provide ID. All he needs is your name and address and the 10 digit MTC number.
Most people have a WU outlet local (mine is a 5 minute walk away). You can get a list of all WU outlets on their website, most are usually in travel agents and banks. I like going down and paying cash, because being a cash transaction I can make it 'invisible' of sorts - I usually give a false name and address, long as I notify the OP of that name /address it's OK, they can collect. I also give only an unregistered pay-as-you-go mobile telephone number. As far as the customer signature is concerned, a simple scribble will do.
All this makes it more difficult to claim back if something goes wrong but to my mind the security makes it worth it.