To answer this question precisely, we would first have to know the nature of the copying. For example, posting similar content on social media wouldn't be enough. However, a change to the logo or the visual presentation of the actual product/service to resemble yours is something a trademark could help with.
The purpose of a trademark is to protect a brand's intellectual property to prevent consumer confusion in the market, so a good question to ask is - do you believe your competition is creating such confusion by the copying you've witnessed?
Nevertheless, even if you conclude a trademark wouldn't help you in this case, we would still recommend registering it to prevent infringement from other parties in the future. A registered trademark would, for example, allow you to send a cease and desist letter asking the competition to stop using the infringing elements/brand.