I have only database for my web hosting, can I

I here in the site http://www.tucktail.com/ you can get the Free Domain name Registration

You can rename your database, but there could be consequences. You will need to modify all ODBC connection strings that reference the old name. If there are no querries or connections to it, then go ahead.

If you have any doubt, what so ever, that there is some application or query referencing the old name, Stop! If you're using a web dev tool like Dreamweaver, perform a sitewide search for the old name to see how much will need to be modified. Then you decide if changing the name is worth that much effort.

Personally, I'm very picky about my scripts and my naming conventions, and I'll do what is needed to have everything properly named. Because, I know that if I don't, I will still want to look for it under the name I want it to be and not the name it is.

I hope this helps you.