I don’t know about whether mastohost supports this or not, but Mastodon definitely allows you to host the service at e.g., mastodon.whatever.com but have your handle be mastodonhandle@whatever.com. This is documented here: https://docs.joinmastodon.org/admin/config/#web_domain
Most web hosts allow you to configure custom DNS entries, so you should be able to create an A record for a subdomain (e.g., social.example.com) that points to your Mastodon server.