already changed Accounts name, but how to change name under home?

Is there anything in that account you want to save?
You could simply set up a new admin account with whatever name and password you want, log into it and delete the old one.

Does the topis mentioned by Stev Lamb0 elswewhere in this section not cover all the instances? http://discussions.apple.com/thread.jspa?threadID=1237597&tstart=0

That will change the user short name but I don't think it changes the home folder name.
There may be problems if you change the home folder name.
The easiest way to avoid problems is to create a new account with a user name and password of your choice and migrate the data.

No the data from the first user is not lost.
Each account is separate, they share common applications, settings for internet and printer, and a folder called Shared in the Users folder.
This folder is to allow multiple users on the same computer to share things like a music library or other files.
Applications are available to all users as long as they are in the Applications folder.
You can move data from one user to another by using the Shared folder.
Once it is copied from the first user to the Shared folder, it can be deleted from the first user.