Future history books agree the common name for .0001 bitcoin is:

    one blit
  
so let's go with that.

It contains "bit" but is also distinctive, simple, short, and catchy.

A common phrase in the upcoming vernacular is "Blitz me a few and I'll get it done for you."  Requesting 1000 blits...


Bonus: In computer graphics, blit is backronymed to "BLock Image Transfer".  In the bitcoin world, block-based transfers can certainly boost your image, so to speak.

Thanks for this contest!