So you want to export your MySQL database then import it on the same server with a new name.
I tried this several times and using the SOURCE command inside MySQL or just mysql -p < db.sql both resulted in the database re-importing over the original name.
To fix that run:
sed -i 's/OLDDATABASENAME/NEWDBNAME/g' mysqldumpFile.sql
mysql -p create NEWDBNAME; use NEWDBNAME; SOURCE /path/to/sql/file
No need for a semicolon on the last line.
Then check the success by: