Step 1: Login to cPanel
Step 2: Enter your username and password. Click the blue login button to log in to the main cPanel page.
Step 3: From cPanel, click on phpMyAdmin. (It should open in a new tab.)
Step 3: Click on the database you wish to rename in the left hand column.
Step 4. Click on the Operations tab.
Step 5. Where it says "Rename database to:" enter the new database name.
Step 6. Click the Go button.
Step 7. When it asks you to want to create the new database and drop the old database, click OK to proceed. (This is a good time to make sure you spelled the new name correctly.)
Step 8. Once the operation is complete, click OK when asked if you want to reload the database.
To make sure database is functioning well for users after the changing of name. You must do the following: