I use many database servers, often with different instances and, of course, users. When you create new connection it is named automatically like "connection to -server-.sde". First of all the "connection to" part is totally needless, it's in Database Connection branch of the tree, isn't it. Name of the server is kind of insufficient and always needs editing. I think it would be really nice if the name of the connection could be defined in Add Database Connection dialog or at least automatically created in more useful way, i.e. server instance user.sde (or server database user.sde).