Alias host names never have any positive impact on SEO. In the best case, they are ignored by search engines. In the worst case, they can create duplicate content, crawling problems, and general confusion for search engines.
You need to make sure that search engines know which host name is your main one and that all others are alternates. See Google Search Central: Consolidate duplicate URLs There are two ways to do this:
- Redirect alternate host names to the main name. This can probably be done by setting up forwarding in webmin.
- Use canonical tags on every page of your site. The canonical tag will have the preferred host name in its URL. If search engines crawl alternate hosts, they would get a signal that the content is duplicate and where to find the preferred URL.
You might even want to use both the redirect and canonical tags. The redirect is a better, stronger signal to search engines than the canonical tag, but canonical tags can take care of duplicate URLs that don't redirect. For example even if
http://ms.example.com/ redirects to
http://music-school.example.com/index.html might be another alternate URL that could confuse search engines but which would be mitigated by canonical tags.
There is no setting in Google Search Console that you can use for this case. The only two methods for dealing with alias hosts have to be implemented on your server.