When we were child the very first questions some elderly strangers used to ask us was:
What is your name?
And, our parents, used to teach us this question in advance with an answer and that experience taught us how to tell our names to people so that they can identify us.
Our names became our identity and we learned to value and appreciate our identities with our names. Today internet names are commonly referred to as domains. The correct form is to ask somebody what is your domain name and not just what is your domain. If you ask a person what is your domain. He can tell you that my domain is Engineering, Accounting or Medicine. As domain means a particular field. But, today, when you say domain it is automatically be thought as your domain name on the internet and not your career or field of activity.
If you go through the synonyms of the word NAME you will find: brand, identity, flag, label, sign and many more but you’ll not find domain as also a synonym of a name. Officially speaking domain is not yet a synonym of name but on internet; name is a synonym for domain and domain is a synonym of name.
Many companies on internet who sell domains have registered their domain names ‘not domain as a keyword’ but name as their main keyword. For example, we have Name.com; NameJet.com; Snapnames.com; NameCheap.com; NameBright.com and I think many more companies have used the word NAME instead of the word DOMAIN.
By this trend I think, the word Domain deserve to be officially be declared as a synonym of the word NAME.