Woot! I have been wanting to do this myself and figured out how to do it, so I thought I'd share the solution. Apologies if this has been done before.
This does require that you have the DA Toolset installed. I also recommend an xml editor application. Many free ones are available.
With XP the default location of the folders/files will be: My Documents\\Bioware\\Dragon Age\\Characters
Before you do anything, back up the file for the character you are editing. I'm just sayin'.
Select the folder for the applicable character and change the name of this folder to reflect the new character name.
Inside of this folder, you will be re-naming the image files and the xml file with your new character name.
Open up the charactername.xml file. Right up near the top, you will see several values with the old character name. These are Name, Folder, Portrait, and Avatar. Change the name value to reflect your new character name.
Now you will go into the Saves folder within the character folder. To make things easy and to avoid possible conflicts, I deleted all but my most recent save. I have no idea if this is necessary, but you did make a backup anyway...right?
Open up the folder for the save you are going to edit. Rename the <char name>.jpg and <char name>_Story.xml files with the new character name.
Open up the <char name>.xml file and change the name as you did with the other xml.
Now you will need to use the Toolset to open up the xxx.das and xxx.das.met files. The “xxx” will be the name of your save. Such as Camp.das if you saved in the camp.
In the xxx.das file, expand SAVEGAME_PLAYERCHAR. Then expand SAVEGAME_PLAYERCHAR_CHAR. In this category locate SAVEGAME_OBJECT_NAME. In the Value column you will see a number string and a character name. ( ######:Name) Double click here and it will let you change the name value. Don't mess with the numerical data, just the name. Save and close.
In the xxx.das.met file locate SAVEGAME_META_NAME. Again, you will be changing the name in the Value column. Save and close.
Now, fire up the game and the character name is changed.

On a side note, I also discovered that this is an excellent way to add special characters in your name. My character's name was changed from Mairead to the correct version Máiréad as you can see here...
Máiréad