Stopping Titles that Overtly Perpetuate Stigma Act or the STOP Stigma Act This bill requires the Department of Health and Human Services (HHS) to issue guidance for renaming the Substance Abuse and Mental Health Services Administration, the National Institute on Alcohol Abuse and Alcoholism, and other agencies and programs with names that contain stigmatizing terms such as abuse, addict, or alcoholic. HHS must also provide Congress with an assessment of the cost of such name changes and recommendations to revise federal laws to rename agencies or programs that are designated in statute.