For Socialtext 2.x and servers without the People module, you can change the Firstname and Lastname displayed for you within a Workspace using the 'Settings' link on the upper right.

If you are using Socialtext People, then you will see a link on the upper right to 'Profile'. From the profile page, you can edit your user profile to change your Firstname and Lastname values.
If your system is integrated with a directory server, then the Firstname and Lastname must be changed in your corporate directory and these options will not be editable in Socialtext.

All users within Socialtext are uniquely identified by their email address. Currently there is not a utility to allow changing this address directly and remain linked to your previous user history.
To change your email address, you would need to be invited to the workspace using a new email address by a workspace admin. You can then use the new address going forward.
An admin can remove the ability to login to the workspace using the old email address from the 'Settings - Manage All Users' page.