Steps to reproduce:

1. Open attached project "811576.zip"
2. In project tab, notice "Light" sprite
3. Expand it and notice multiple sub-sprites that were created by slicing it
4. Rename sprite from "Light" to "Dark" and notice that child sprites aren't renamed

Note: Setting Sprite back to Single, applying settings and then setting it back to Multiple doesn't help - sprites are still created as Light_0, Light_1 etc. Reimporting sprite doesn't fix this as well. Basically you have to delete sprite and reimport it to Unity from scratch (loosing all you settings, etc.)

Reproduced with: 5.2.4f1, 5.3.5p7, 5.4.0b25