Not having a choice of last name has driven people to the kinds of choices you end up making on other systems that ask for a user name/login id, i.e. appending a bunch of digits to a name to ensure uniqueness. A display name will hide such names... mostly... but can't be counted on to be unique, and the underlying name has to be used where one must uniquely identify a resident. For example, my hug/kiss attachment won't work with display names.
Worse yet, the divide between old and new naming seems to have created a class division in Second Life, and some argue that it's harder to feel an attachment to SL when you're just Joe1234567 Resident.
The JIRA entry requesting true last names, SVC-7125, has 2,136 votes and 696 watchers as I type, but has sat unresolved since its creation in July... but now there may be hope. A recent comment points one at this from Rodvik Linden. To quote:
Last names under active discussion. We are trying to figure out how to do it in a way which would be excellent rather than just ok. We want it intuitive with extra features. Hopefully we will roll out what we are thinking early January latest.I'm looking forward to seeing what they come up with, and especially whether all the current <line noise>
Identity is very important so as we touch it we need to make sure we are adding something great.