Do I Need To Send A New Email Asking For No Contact To Abuser Using New Email Address To Harass Me?

I have been no contact with my abusive mom for about five years. I sent her an email at that time saying I don't want her to contact me. My younger sister has been no contact with her for 9 years. Sister and I keep in touch once per year for a safety check. Our mom continued to harass us consistently in that time until November of this year. She sent us an email saying she was changing her name, getting rid of her email address, selling her house, moving to another state. On Monday, she sent us an email under her new name with her new email address, signing the email "Mom" and referencing herself as the person who gave us life. Do I need to send a new email to this new address asking her not to contact me anymore?