changing server - copy all files and DB - need help !

[lior_avr]

Dear members
Joomla sysytem -
Today I try to hosting my website at a new server.
Well I tell tou what I done and tell me if I wrong or how should I need to do it:
1) I download all the files and folder form the old server to my pc and upload them to the new server – AS IS.
2) Database – I connect to my old phpmyadmin and backup automatic all the db to zip file. Then I upload the zip file by import to my new server.
At the old server there were 55 tables and when I upload for the new one there was the same.

Now after all this I connected my new server in index.php by domain and I got error.(I done it at several servers and all the time there are different error.)

Should I change any properties at the files (configuration? Index?) After I change server?
Please try to help me with that.
By the way: the name of the DB at the old server was: holonib_holoni
At the new server the DB name is default from my server like: lioravr_holoni
Is it matter?