Star Wars: The Old Republic is abolishing this practice next month. Starting on April 2nd, 2013, players will be able to log into their accounts -- both game and website -- using only their display name. That makes knowing your display name crucial! For those who can't remember theirs, it's displayed on the top right-hand side of the home page after you've logged in, so make note of it before the email login disappears.
In the announcement email sent to players, BioWare explained that this measure was implemented to "increases the security of [the] game authentication system, which helps continue to keep the game protected from many security threats including account takeovers."
[Source: BioWare announcement]