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You may have to request that your webhost setup your MySQL database for you. I have had 2 webhosts in a row where that was the case. You email them, or if you have live support, request that they setup the MySQL database.
Like naming a kid, they can call it whatever they want, say something like BIGSKY_COM or PHPDUDE .
Once they have created the database and give you the name of it, you then go back to your XOOPS installer and enter that database name in there.
If your database was named PHPDUDE, then put that exact name in the installer where it asks for it.
If your control panel allows you make your own databases, then create one for XOOPS called XOOPS_DB or something like that and go back and enter that into the XOOPS installer.
Get the idea ?