I also noticed that im my old server I had a home/name

and in my new server it has a home/different name ( my websites name)

if I make a backup from godaddy and the backup includes my original name at the end when I try to restore from a backup homedirectory files will it work if there is a different home/name in the new server ?

I believe this link would be useful for you: https://docs.oxwall.org/faq:how-to-transfer-my-site-to-another-hosting

define('OW_URL_HOME', 'http://ow/'); //new site URL
define('OW_DB_HOST', 'localhost');         //new database host
define('OW_DB_PORT', null);                //new database port
define('OW_DB_USER', 'root');              //new database user
define('OW_DB_PASSWORD', '1234');          //new database password
define('OW_DB_NAME', 'ow');                //new database name

thanks for the reply ross, I spoke with the arvixe team and they migrated all my files and database to the arvixe servers, so I guess the database name issue is taken care of, I don't know how to explain it is like the arvixe cpanel forces a username_ in front of what ever database you are trying to create or name, taking in account the above information where can I find such information to update that file. I remember godaddy was localhost but for arvixe does it change ? if it does what changes and what stays, I need some help with this. appreciate your support.

Also, before importing your old database into new one, you have to create that new database, which is why it has the password and new credentials. 

Have you checked the link I provided to you: https://docs.oxwall.org/faq:how-to-transfer-my-site-to-another-hosting ?

While the files are transferred over as they are on another host, the structure of the database naming can be different. With cPanel we use the username_database name as it allows any database name to then exist. With the GoDaddy structure two people on the server could not have their database name as "oxwall". With Arvixe it would be username_oxwall. Do you have a ticket number that I can reference? It sounds like your user name just needs to be added to the front of the user and the database:

define('OW_URL_HOME', 'http://ow/'); //new site URL
define('OW_DB_HOST', 'localhost');         //new database host
define('OW_DB_PORT', null);                //new database port
define('OW_DB_USER', 'yourname_root');              //new database user
define('OW_DB_PASSWORD', '1234');          //new database password
define('OW_DB_NAME', 'yourname_ow');                //new database name

Thank you!