IMO, I believe that the namesake is not that important because the name or a brand can be built over time if you have a good use case and working products or even services to offer and for me, it can be a distinction.

Anyway, Doge Chain is a good name because Doge is already known and popular among many crypto users, so it's an advantage for the project but it's not enough the team must show to the crypto community that Doge Chain is a separate project with different and unique use cases to offer that can drive the demand of its token, and far from its namesake Dogecoin and popularly known as a meme coin or a joke!