I bought a Compaq laptop at PC world and the e-mail address they programmed in for is a bit specific (ie my full name etc) how do I change it ? I am computer illiterate.

Where do you need to change this e-mail address ?
If it's your username on this computer there's no need to make any changes.

My e-mail address contains my full name. I was advised this leaves me open to scams.(a little patience here, I am 66 years old, and a bear of very little brain)

Who created this address for you. There is nothing wrong with using your full name, depending on what you use the e-mail address for. I have several e-mail addresses that use my real name.

What is the domain part of the address (after the @).

If you want to create different addresses you can go to Gmail.com, outlook.com, Yahoo.com or several other web based free e-mail services and create other e-mail accounts.

Also it is a good idea to have several email accounts. A private email and primary email as well as 1 or 2 "throw away" accounts. The throw away accounts are when your seeking general information and its low on importance but high possibility of spam. Like some rewards programs and such.