A little late to the party, but I think the advice here is really solid.
I do think communities generally benefit from having their own identity, but it also depends on the role the community plays. If it’s exclusively for existing users or customers, keeping the name closely aligned with the parent brand makes sense.
Many of the communities I work on, though, are designed for lead generation. In those cases, the community has its own name that’s connected to the company’s space or mission without being the company itself.
For example, my business serves endurance athletes, and we run a community called Endurance Nation. Someone who isn’t yet a customer may not feel like they belong in our company’s customer community, but they’re happy to join a community focused on endurance sports where they can learn, connect with other athletes, and participate in the energy we’re creating.
In that sense, the community becomes a third space, a bridge between prospective customers and the company itself. We call it The Sweet Spot (a play on a type of workout that endurance athletes use). This is not our company branding in any way…but sharing for reference.