“Please only add common names which already exist, and please follow the Guidelines for adding common names. Please do not make up common names.” (https://forum.inaturalist.org/t/how-to-add-a-common-name-to-a-taxon/9792). It is a grey zone, as mentioned by @pfau_tarleton and hence the discussion on inventing common names on iNat reached some 200 posts and you can likely find thousands of posts on iNat forum on this topic.
I’d say that in this case a common name proposed in a research paper is deeply in the territory of “already exist” so to me it sounds as a straightforward case of implementing it into iNat.
Just a note: the topic is a rabbit hole :) The topic you mentioned (https://forum.inaturalist.org/t/common-names-invented-on-inat/27452) was specifically addressing the role that iNat and iNat users should play in creating and disseminating common names to public. The iNat guidelines are that iNat users should not generate new common names but there is no general definition for an “existing common name” in iNat guidelines. So currently it all depends on iNat users and whether they want to add a name into the field “common name” and on curators and whether they want or have the capacity to revise the common names.