How to start a hashtag?

I just saw a post by a teacher on Twitter, a new user. She asked:

Does my school district have a hashtag? Should it?  

I think it's a great question. Sure, some people create lots of hashtags but I've never read anything that addresses this context.

First of all, hashtags are like words. Anyone can create one just by using it. But mostly, they don't get picked up and create much of a discussion or community

Most hashtags that people create are pretty limited and don't get picked up.  I've seen hashtags like #wearingabowtie , #fellonpurpose , and #HSMP (homeschool me, please!) which did not get much popular use. Then there's the ones that have gone viral such #metoo

Also, it's a little different for a teacher who wants to create a hashtag for her district since the obvious hashtag, the schools initials, might have compliance or IP issues about it. For example, MiamiDade Schools (near where I live) are routinely known as MDCPS (Miami Dade County Public Schools). Their Twitter handle is @MDCPS.  So, would a private individual who starts using MDCPS as a hashtag be infringinon a copyright or trademark? I think yes if they used it for anything other than the obvious but also, there is virtually no enforcement so there's nothing to worry about. 

But, what if you were a new teacher working for MDCPS, should you then take a chance to start using #MDCPS

School districts of course are pretty strict hierarchal places and I'd be a little careful as a new teacher in doing such a thing. I might ask the district twitter account, perhaps by PM, what they think.