The story
Blend of epi(mer) (“a type of isomer”) + -rubicin (“daunorubicin derivative”). However, the molecule is in fact an epimer of doxorubicin, not daunorubicin. Thus an etymology as epi(mer) + (doxo)rubicin is plausible as well. See libfix for information on affixes such as -rubicin.
Etymology from Wiktionary, CC BY-SA 4.0.