Since the death of popular dad-blogger Oren Miller in February, there has been a resurgence of an initiative he started: pushing Amazon to change its parenting program’s name from “Amazon Mom” to “Amazon Family.” Amazon Mom is a subscription-based service that allows parents to get deals such as 20% off diaper subscriptions and 15% baby registries. Members also receive emails with messages like “As a busy mom, your time is precious. That’s why we....