If you are using mysql, The data base username and data name are not the same. Not fimiliar with godaddy, but some where on the control panel u should be able to create data base users  and data bases(shcemas). create a user (username and password) login as that user and create a database for elgg. you can name it anything you like.

Now your settings should like something like this.

Database username

$CONFIG->dbuser = "name you picked";

 Database password

$CONFIG->dbpass = "password you picked";

 Database name

$CONFIG->dbname = " I suggest something easy like elggdata";

Database server

// (For most configurations, you can leave this as 'localhost')

$CONFIG->dbhost = " this should be the location of your database on godaddy"; 

Database table prefix

// If you're sharing a database with other applications, you will want to use this

// to differentiate Elgg's tables.

$CONFIG->dbprefix =  you can just commment this out by adding // before it.

IF you are editing your setting file by hand please uncomment this entire section and save the file as setting.php

Hope this helps!!! 

Thanks Hottie, but here is what my host says about the databases.

NOTE: The database name and username will be identical for all newly created databases.

Sorry about the font its a cut and paste. When I go to my database admin panel, is says I have one database, but when I open the php mysql control panel there is a second database called information_schema. Is that supposed to be there, I am not sure.

yes it is that is the default tables of mysql to keep up with your input info. Things such as the name of your new database.

Are you still having problems. How can I help 

If you want me to take a look send me your site info .

ffrinfo@yahoo.com