The gym is a single entity rather than a plural, so it’s correct to say “my gym does a CrossFit class” or “my gym has a pool”. I don’t think you’d find many people who’d do that differently to be honest!I’m always interested in British grammar for entities. Brit Tats: do you not say “my gym does” vs “my gym do”?
When we’re referring to a named company, we often view it as a group of people and so will apply the plural verb form. So we’d say, for example, “HSBC are a large organisation”. It’s not a hard and fast rule, and it tends to depend on whether we informally see a firm as just a firm or as a collective of people.