If you look through topics created 4-5 years ago, you will find quite a few suggesting to divide Bitcoin further (as if it could help its price), as well as discussing different names for different subunits of a whole bitcoin. Does it make any sense? I guess not much as the lowest sensible denomination would still be defined and determined by the amount of fees required to confirm a Bitcoin payment within a reasonable timeframe. And that, as of now, is about a few thousand satoshi, which turns the whole idea into an exercise in stupidity and futility
The question is being raised again and again, because Bitcoin is having a disadvantage with both its name and its sub-units. First let's take the name. The "coin" part gives an impression that it can't be further subdivided, when in reality nothing can be farther from the truth. Especially the newer users are getting confused by this name.
Now coming to the units, one Bitcoin is being subdivided in to 100 million Satoshis. There is nothing in between. mBTC is an informal unit, and it doesn't have a name of its own. A few names were suggested for mBTC, but there was no consensus. And we need smaller units badly now, as the exchange rates have surged past the $10,000 per coin level. Even mBTC may be too big for practical purposes now.