As the owner of older rights in the name someone registered and/or uses as ENS address, can I ask platforms to block the relevant token from being displayed on their platform?

Yes, that is advisable. Consider this equivalent to a notice and take down message you would send to the platform owner in web1 and web2. In case it does not follow your request, the platform may be liable itself for infringement (or support thereof), which may at least give you access to damages.