BC's showing off the new tattoo she got over the one she partially erased -- Future's name. In its place, she put her daughter Dream's name. That relationship should last longer than the one with the rapper.

The doting mom's now keeping both of her kids handy. King's name is on her other.

TMZ broke the story ... Future dug the tat when BC got it in 2015 barely a month into dating. She's since been with Rob Kardashian and others.

Unclear what took so long to wipe it off, but lesson finally learned?