When you are using the web to make a purchase or sign up for something that you are completely familiar with using your real name and address is fine. All to often we don't know about the company on the web or who we are talking to in a chat room. In those instances for you or your kids, using your real name on the web can lead to problems. I use a pseudonym and have found out first hand how my surfin' the net gets my name on more mailing list than you can imagine. If your kids use a chat room it is very important that they do not use their real name or provide their actual address, school, birthday or any other information about themselves.
Most service providers offer additional email accounts at no extra cost.
I am one of those people who sign up for almost anything. The web has changed that flaw in my character. I try to be very careful of what I sign up for. Even being careful causes me problems. I ended up signing up for the same monthly service twice.