A reminder from Checkup says something like “A checkup is due for Mei”. It doesn’t say which one. That’s on purpose.
Lock screens are public
Your lock screen is seen by the person next to you on the train, by colleagues when your phone is on the desk, by family at the dinner table. A notification that says “Mammogram due” or “HbA1c test overdue” tells all of them something about your health, or your child’s, that you didn’t choose to share.
So by default, a Checkup reminder names only the person. You know what it means when you open the app; nobody glancing at your phone does.
You can choose otherwise
If your phone is yours alone, names can be handy. Turn on “Show checkup names” in Settings, Reminders. It’s off unless you switch it on.
Scheduled by your phone
Reminders aren’t sent from a server. Checkup asks your phone to show them on certain days, at 9 in the morning: a month and a week before something is due, on the day, then weekly if it’s overdue. So no company, including us, knows what you’re being reminded about, or when.