Yes, if someone has been using a name that you are attempting to trademark for a significant period of time, they may have certain rights and could potentially oppose your trademark application or challenge your ownership. Unregistered trademarks, or in some jurisdictions - common law trademark rights are acquired through continuous and consistent use of a mark in commerce, even without formal registration.
In such cases, the existing user of the name may have grounds to challenge your trademark application or claim prior ownership. They could argue that they have established trademark rights to the name before and that your use of the trademark would infringe upon their existing rights.
Resolving such conflicts can be complex and may involve legal proceedings or negotiations to determine the scope of each party's rights and the potential for confusion in the marketplace. Factors considered in such disputes include the geographic scope of each party's use, the nature of the goods or services involved, the duration and consistency of use, and evidence of consumer recognition.