What does Screen Name mean?
A screen name is simply a name that a user chooses to represent him or herself when using some application. It could be a social media site, an instant messaging application or some other kind of collaborative application. While many screen names are pseudonymous, some services require users to use their real names. This is controversial because users often want to maintain their privacy, but real name policies might make them less safe.
A screen name can also be known as a username, handle, nickname or nick.
Techopedia explains Screen Name
A screen name is the name that users choose to identify themselves on a network. The network could be anything from an IRC nickname to a Twitter username.
Many users choose to either use their real name as the basis for their screen name, often in a shortened version. For example, John Smith might choose the screen name of "jsmith." Other screen names are pseudonymous. These screen names can be quite fanciful, based on things such as users' favorite books, movies or TV shows.
Some online services require users to use their real names or face being banned. Google+ originally had such a requirement. These real name policies are controversial because some users might face discrimination and harassment, such as over their sexual orientation, gender identity, religion or race, simply for using their real names. When this extends to offline harassment, these people have justifiable fears for their safety. This is the basis for the "nymwars," or arguments in favor of pseudonymity.