Hi @Yannick40 If this is the first problematic guest you have had with over 20 positive reviews, then you are a lucky host, right? Now is the time to become more educated about the business and you have come to the right place. So many experienced hosts from all over the world post on this site. I admit I learn more than I educate 😄
Anyway, your post asks the question about naming faulty guests. I wonder if you have looked at a potential guest profile to read the reviews of that guest. Reviewa arre a good indication of the guest behavior, not fool proof, but helpful. When you write a review for this guest, if the damage was malicious and due to breaking rules, you would give the thumbs down recommendation. If you think the damage was an accident by an otherwise good guest, no need to have negative review. If the guest does not accept responsibility for the damage and pay for the claim, your review could include a statement such as, "better suited to a hotel than to the shared home environment." Other host will know what you mean.
I do have another question. In reading your reviews which are very positive, one guest commented a negative experience with bedding that was smoky smelling. While your listing has the rule of no smoking, did you have a guest that smoked? If you recognize that the guest experience of smoke odor was not made up, your "blaming" the guest for not letting you know about the problem, in your response, does not reflect you as a caring host. It is good to realize your response to a review is always an opportunity to demonstrate your great host skills and not a good place to be defensive about a negative comment.
Good luck with the damage claim and your continued success with the business.