How are you trying to get the assistance - via Messenger or email ?
Messenger is the simplest way. Remember that if you're using a dial-up connection then Remote Assistance depends on your IP address, so if you disconnect after sending the request and then reconnect you'll probably have a different IP address - so they won't be able to connect. It also has a time limit to enable connection (I think it's about 10 minutes). In other words, arrange a time so that the person will receive the request straight away. If you're using broadband with a fixed IP address then this won't be a problem.
I'm not too sure what "name" you're talking about. Is it the PC's name or the User Account name ?
What error messages are appearing (at either end) ?