When you tell a story (preferable your own) you should be precise, accurate, and original. So… YES, you should coin new terms through your story telling, and if yours is a clever one that gets attention, it can be good for branding too. For example, I coined the term SMI, for “social media influencers” because:
b. “Influencer” is not always accurate, and I never liked that term
a. I focus on #socialmedia
And you, what term will YOU coin?
PS/I also coined the term BSMP (Branded Social Media Profile)
SMI* = Social Media Influencers