I guess your intention might be to give a name to your biological mother although she passed away. You may or may not have following in your mind based on your consideration:
1) Your biological mother won't receive any immigration benefit (for a reason that so obvious)
2) You implied you sub-mitted a fraudulent document to USCIS (your birth certificate should list your biological mother)
3) Your step mother may become ineligible to receive immigration benefit
Do after you think.