Responsible Person for your CE-marked products

We have around 90 items that are flagged as requiring a responsibe person, approx 40 of these don’t require a CE mark, we opened a case with SS asking them to look into it, they asked for a couple of sample ASINs…
They responded indicating that out of the 3 ASINs given, 2 (a notebook and a Yankee Candle shade/tray) do not require a CE mark and the 3rd (an adult swimsuit) does require one.

They didn’t do anything to fix the 2 that don’t require one though…

That’s correct, the full list of items requiring a CE mark is here: https://www.gov.uk/guidance/ce-marking#products-that-need-ce-marking
Clothing isn’t on there, the only exceptions (some of which would be debatable) would be clothing designed to serve some medical purpose (i.e. doubles as a back or neck brace), clothing with electronic parts (i.e. LED lights), or clothing that could be seen as a toy designed for children (i.e. fancy dress)

If you are the owner of a given brand, you can enter the details for the entire brand, otherwise you have to do them 1-by-1, if the brand owner does enter their details, you no longer need to enter them yourself. If anyone else besides the brand owner enters them, you still have to enter them too.

It’s worth pointing out that the responsible person’s details must be on the product packaging or somehow included with the product, so if you don’t own the brand then the responsible person is normally the EU-based manufacturer or importer (the “person” can be a company or trademark name) that should already be indicated on the product packaging.
If these details aren’t on the product then and only then do you need your own responsible person based in the EU and you need to put their details on the product packaging or on a leaflet/etc. included with the product.
This person also must be in possession of a certificate of compliance for the product as well as have knowledge of the product.
There’s nothing to say you can’t just use your own person from the start but then you have to re-label the products, just creating more work for yourself.