Can see other user's databases in shared hosting
I'd talk to your hosting provider's technical support people about this and get them to explain to you the security configuration they have on the msdb database, which is where those details are stored.

By itself, the list of database names likely does not indicate a security risk.  I'd ensure I wasn't giving away any details in my database names.

If I had SQL Server Agent Jobs running where the output was logged, I'd probably be somewhat concerned about others being able to see that output, so I'd confirm that (a) I don't have SQL Server Agent jobs with output, and (b) no one else can configure SQL Server Agent jobs to run against my databases.