Comment by Volundr

You can absolutely say "I work for X". Otherwise resumes don't work, forget LinkedIn. Telling people you work for X is not the same as claiming to represent X.

The exception here is executives and maybe in some instances management, where they need to be careful what they say because anything they say may be construed as representing the company. But having on your social media that you work for X and having other posts where you talk about normal social media things? 100% fine as long as your don't say something along the lines of "I work for X and our official policy on Y is..." (i.e. claiming to represent them)