Effective 3/31/2018 PrimeMail by Walgreens Mail Service will operate under the name “Alliance RX Walgreens Prime“. Prime + Walgreens assures customers that only their name is changing. AllianceRX Walgreens Prime promises to stay consistent with their standards for communications, prescriptions, refills and service. Employers who have health plans with Horizon Blue Cross Blue Shield of New Jersey should notify their employees of this change.