Keeping a period tracker private on a shared or borrowed phone
If someone else uses your iPhone, or might pick it up, these iOS settings keep a period tracker out of view. None of them needs a particular app.
Lock or hide the app
From iOS 18, touch and hold an app's icon and choose Require Face ID (or Touch ID or passcode). Choose Hide and Require Face ID to remove the icon from the Home Screen; the app then sits in a locked Hidden folder at the bottom of the App Library and its notifications are not shown.
Notification previews
Settings, Notifications, Show Previews: When Unlocked or Never stops reminder text appearing on the Lock Screen. You can also set this per app under Settings, Notifications, then the app.
Widgets and Live Activities
Lock Screen widgets and Live Activities can be read without unlocking the phone. Use an app's discreet wording if it has one, or keep cycle widgets on a Home Screen page instead.
Search and suggestions
Settings, Apps, then the app, Siri: turn off Show App in Search, Show Content in Search and Suggest App so it does not appear in Spotlight or suggestions.
Calendar events and shared calendars
If you add estimated dates to Calendar, keep them in a calendar that is not shared, and give the events a neutral name. The period calculator on this site can name them "Reminder".
In Isla
Settings, Kept on this iPhone: App Lock asks for Face ID, Touch ID or the passcode; Discreet wording keeps the word period off widgets, reminders and the Lock Screen countdown; and a discreet app icon replaces the usual one.