I have no claim to the word skin. To be certain one must be able to carefully consider law and facts. The next step is to prepare facts and law so this won't reoccur. Different trademark classes of goods and services exist for different products and services - therefore it is indeed possible for two different traders to use the same mark under certain circumstances. I believe I have infringed on an existing service mark.
Loreal company has a service mark on the word skinlogics.
It was for products for facial scrubs, and toners. My service mark was for my skincare facility which provided skincare services. The name I chose was not a plural but skinlogic. I have no claim to the word skin. To be certain one must be able to carefully consider law and facts.