There is no copyright in a word or short phrase because it lacks the necessary creativity to be considered a "literary work".
The concept that could apply is a trademark.
Trademarks must be registered and ...
the application must also contain a list of goods or services to which the sign would apply.
Anyone can use a trademark to promote goods or services in a field for which it is not registered and can seek registration in that different field (which the original holder would object to, probably successfully). Remedies for infringement can include an injunction and damages or an account of profits.
In addition, unregistered trademarks (and registered ones too) may be protected by the common law remedy of the tort of passing off which requires the plaintiff to prove:
- they have reputation or goodwill in the trademark
- the defendant has misrepresented such that the public is liable to believe that the goods and services offered are offered by the plaintiff
- the defendant's conduct has or is likely to result in damage to the plaintiff
Remedies are the same as for trademark infringement but the plaintiff has more to prove.
In addition, in some jurisdictions (e.g. Australia) there may be statutory prohibitions on "misleading and deceptive conduct" which are available to both the offended party and the state.