joepa60 Not an expert. I don't think you can force them to stop without a trademark on the prefix. I would start by asking them to stop using Blooms. They may or may not know your family has been using it. If you want to try to trademark "Bloom's" Look at "Coseytown" for an example on the USPTO website. It might give you an idea of how to fill out the paperwork or get a lawyer to help you. I believe the paperwork will ask you for how long it's been used. Per the ADS it looks like Bloom's Kenn and Bloom's Sylvia date back to 1981. (or maybe Copyright)
The use of prefixes has become a topic of conversation. A few (under fiveish) don't want their cultivars sold or traded either at all or without compensation. Just my opinion, even if one favors the free dahlia market, it's probably a good idea to protect the Prefix in some way.