Is it legal for a company to use a variant of its company name - an acronym, abbreviation, etc - on social media without registering that name as a business name?
I think you'll find that abbreviations, acronyms and derivative terms
(even if not separately registered, let alone not separately trademarked)
are not usually a problem.
What's the back story to your question?
Also, just to be clear: You may not quote, rely, or refer to anything I say on here, in your own blog.