If someone's been using the name I'm trademarking for years, can they fight me for ownership?

Yes. Prior use of a mark, even without formal registration, can give the earlier user grounds to oppose a new trademark application or challenge a registration.

In first-to-use jurisdictions like the US, prior commercial use establishes common law rights in the mark. A business that has been using a name in commerce for years can use that prior use as a basis for opposing a later applicant's registration, provided they can demonstrate the use was genuine and predates the application.

In first-to-file jurisdictions like the EU and UK, the grounds are narrower but prior use is not entirely without weight. A business with a well-established reputation under an unregistered mark may be able to bring an opposition based on passing off or earlier unregistered rights, depending on the jurisdiction.

The practical implication is the same in both systems: conducting a trademark search before filing, including checking for active unregistered use in the market, reduces the risk of this kind of challenge.