Trying to phpMyAdmin import a database with a different name
There are two possibilities here; the easier one is to use phpMyAdmin to change the name on export.

To do that, you'll need to select the "Custom" radio button on the export page, then under the "Output" section look for "Rename exported databases/tables/columns" -- by selecting that checkbox, you get a dialog box to rename the entire database or specific tables or columns. 

The other way is to edit the .sql file and find the references to the old database and correct it with your text editor. It's probably only the initial CREATE statement and USE very shortly after that.