I don't understand..
..."basically there is no name for a database ? just a place to store data ??
and mySQL, SQLserver is the DBMS to retrieve the data ?"..
a database is an amorphus area on disk that stores data. the database engine is effectively asked questions (SQL Queries) and retrieves the data from a database.
a database engine can have many databases stored within its control. each of those databases will have a name, but usually I'd expect one db per company (or per package the company buys). The name of the database within the sql engine will reflect its function (eg personell/HR) or its vendor (eg SAP),
if its a shared web server db I'd expect the operators of the web server (the ISP) to create distinct dsatabases within their data server(s) which are named after the customer or the application.
when you connect to most servers you have to specify the database sever you want, the name of the database within that server. each datastore in that database (usually RDBMS's store data in tables) wil have a unique name, and within that table you wil have columns which uniqeuly identify an attribute
if you want to go into the mechaics of relational databases do a google on normalisation but these two references are a pretty good starting point
www.r937.com/Relational.html
http://www.tonymarston.net/php-mysql...tml#2005-08-12
both of those sites have lots of other 'good' stuff that may be of interest