Comment by chao-

Your concern is valid, but you are misguided on a few details. I will inform you as best I can in the context of US intellectual property law.

I am not a lawyer, but I have spent a lot of time adjacent to this stuff, and am not aware of a "copyright strike" as a legal concept. I assume you are borrowing this terminology from various platforms who have their own internal "three strikes" policy for user-created content that violates copyright. However, those policies are entirely for-and-within those ecosystems, and do not directly correlate to any legal notion of "copyright strike". If you violate the rights of someone's work, they send you a C&D and/or sue you, regardless of the platform's use of some "strike" system.

That "someone's work" is key: Copyright covers the output of creative works: writing, art, photography, code, music, video production, et cetera. Copyright law would apply if social media Kith stole an image from fashion Kith's website. It would also apply if one was sent social media Kith the source code from fashion Kith's website, and social media Kith used it (I don't know why they would, but it would violate the copy rights of fashion Kith). The violation would be about the work, not the name.

You referred to the brand name, which would be covered by Trademark law. Trademark law concerns itself with more than just the name, but also the design/logo, sound of the name when spoken, etc. Within that, there is a focus on the likelihood that the public would might confused and the degree to which one brand or another might be damaged by that confusion.

This leads to (somewhat common) situations where there are two marks with the same name, but in different industries, because there is no risk of brand confusion. For example "Delta" is a trademark of an airline company, and "Delta" is also a trademark of a faucet company. They have different logos and products/services in different industries (the USPTO has 40-or-so categories), thus there is little risk of brand confusion.

On the other hand, if two businesses have products/services in the same category, even a different name can be a Trademark violation if it (for example) sounds similar enough. Imagine a hypothetical hard drive manufacturer named "StoreTech". If you started a hard drive manufacturing company and named it "StorTek" it's very likely that StoreTech would pursue trademark action against you, even though the name is technically different!

There is A LOT more to Trademark than just this, but these are some factors to keep in mind.