First of all, what are Display Names?... Display Names is a new feature designed to allow users to create a name of their choice. Not to be confused with a (user name). The user name is the name you signed up with to LL. This is the name you sign into the viewer with and this cannot be changed.
A Display Name can be just about anything up to 31 characters long. Only people on viewers that support display names will be able to set and see display names on other avatars. If you are on a viewer that supports display names, there will be options to see either display name only, display name AND user name, or just user name. If you have display names enabled, while on LL V2, the chat you see from users who have a display name set will reflect that display name and not their user name (from what I understand). If your on a viewer that supports display names, and you have it set to only show display names, you can always open a users profile to see their original user account name.
The next release of Phoenix Viewer expected out in the next few weeks will have support for display names a well, however you will have an option to list users in chats by their user name, display name & user name or just display name.
There has been a lot of negativity surrounding Display Names, and while I don't entirely agree (personally) that display names are a great idea, I will say that they are NOT evil! They do have some good use cases like for Role Playing, or simply fixing a typo in your user name. Married couples can now have a common last name, etc. Yes, display names can be abused and used for malicious behavior, however this is no different than most any feature in SL. The vast majority of users will be using display names appropriately and as they were intended to be used.
I've heard reports first hand that people are passing out scripts that auto ban anyone using a display name. While land owners do have the right to ban/eject anyone they wish for whatever reason they choose, I strongly urge people not to do this to users just because they have a display name. There are many valid reasons and uses for display names and I suspect a lot of people will be using them. However if you see someone who has set their display name to your account name, with the intention of impersonating then I would strongly suggest you abuse report them. Ejecting and banning accounts who do this from your land.. in that case.. I think would be reasonable.
NEW ACCOUNT NAMES
LL has made some changes to the sign up process. No longer will last names be available primarily because Display Names allows users to create whatever name they want. Old accounts signed up with a (firstname lastname). New accounts only have a first name and the last name is automatically "resident". This has caused a lot of confusion among people who have recently signed up with one of these account names and dont know how to log into older viewers that have a (Firstname Lastname) login field. Simply login with your first name, being the name you chose when you signed up, and use "resident" as your last name. For example, if your username is thejoesmith: First Name: thejoesmith Last Name: resident
Old users who have a firstname lastname might notice that logging into secondlife.com website no longer has firstname and lastname fields. You guys log in using firstname.lastname. So for example I log in as jessica.lyon
I hope this clears up some of the mass confusion going around about display names and new account names.
Here are some links with more information.
LL Documentation on display names: http://wiki.secondlife.com/wiki/Display_Names
Must see Torley Video on display names: http://www.youtube.com/watch?v=eGoHjGz2OaQ
A must see follow up Torley video on Display Names: http://www.youtube.com/watch?v=JNH-3IPTrjc
Documetnation on SL Usernames: http://wiki.secondlife.com/wiki/Usernames