You would need to modify the MySQL database permissions to prevent them access to particular databases. Note also that when you do limit the databases a user has access to, phpMyAdmin won't show them in the list of databases.
4.5 Is it possible to let users create their own databases?
Starting with 2.2.5, in the user management page, you can enter a wildcard database name for a user (for example "joe%"), and put the privileges you want. For example, adding SELECT, INSERT, UPDATE, DELETE, CREATE, DROP, INDEX, ALTER would let a user create/manage his/her database(s)."
The above was from the docs:6.20 In MySQL 4, I see a lot of databases which are not mine, and cannot access them.
Upgrading to MySQL 4 usually gives users those global privileges: CREATE TEMPORARY TABLES, SHOW DATABASES, LOCK TABLES. Those privileges also enable users to see all the database names. See this bug report.
So if your users do not need those privileges, you can remove them and their databases list will shorten.
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