"Bits" is just a slang name for µBTC (microbitcoin).  The value is exactly the same.

If you don't like the slang name "bits" then invent a new slang name and popularize it in your community.  Perhaps call them microbits, micros, or mikes, or micks, or you-bees.  The name really doesn't matter as long as its in common enough use to avoid confusion.