Decide what you are protecting
A shared iPad in the living room, study or guest room is useful, but it is not a proper private multi-user device. Start by deciding whether you only want fewer interruptions or whether you need real separation. If the problem is visible pop-ups, notification settings may be enough. If nobody else should access the conversations, the messaging app must not be connected to your private account on that iPad. Hidden previews protect you from quick glances on the lock screen, but they do not stop someone from opening an unlocked app.
Turn off iMessage on the shared iPad
If you do not need messages on that device, open Settings -> Apps -> Messages and turn off iMessage. Then check Send & Receive and make sure your private phone number or Apple Account email addresses are no longer active there. If you use text message forwarding, review that as well. The goal is simple: personal conversations should never arrive on the shared iPad in the first place. Apply the same logic to WhatsApp, Telegram, Signal and other messengers. Do not leave them paired on a device that sits around the house.
Make notifications less revealing
If you want to keep a messaging app installed, open Settings -> Notifications and choose the app. Remove lock screen alerts, turn off banners, or allow badges only. Set previews to never show, or only show when the device is unlocked. This is a good everyday fix when children use the iPad for games, someone checks a website, or a visitor quickly looks something up. Just remember the limit: notification settings hide the alert, not the account. If the app is signed in and the iPad is unlocked, the messages may still be reachable.
Set up family devices deliberately
For a truly shared iPad, a separate Apple Account or neutral family email is often cleaner than using your private main account. Use Family Sharing, household profiles and separate media profiles wherever the app supports them. Private iCloud photos, calendars, contacts and messages should stay off a device that other people use casually. Recheck this after restoring from a backup, handing down an old iPad, or turning a personal device into the family shared tablet.