PHP Execution Timeout and Hosting Company

I need to increase the execution time for PHP scripts on my 10 page, 60+ and growing blog posts website. I need to know who exactly is hosting my website. It’s on WordPress. The domain is registered through Enom and the domain itself is being renewed on Siteground, but Siteground is not actually hosting my website. I think WordPress is hosting it, but there is another company involved that is actually hosting my website through WordPress.

I need to know what company other than WordPress is hosting my website. I also need to contact them and ask them to increase the execution time for PHP scripts.

Here is the error message from BackupGuard:

BackupGuard Error: PHP EXECUTION TIMEOUT ERROR

Your hosting has an execution time limit of 30 seconds for PHP scripts, which is not enough for performing a full backup/restore of your website. A full website backup/restore is a complex process which may take a couple of minutes depending on many circumstances. The needed execution time varies depending on the backup options and your server performance, that’s why we cannot tell exactly how much execution time is needed. But, almost all hosting providers give users the ability to increase the execution time limit or they increase it themselves, upon user request. Please ask your hosting provider if they are able to increase your execution time limit.

The page I need help with: [log in to see the link]