To hide a name from appearing on Instagram when you search for it, you can follow these steps:

1. Clear your search history:

   • Go to your profile and tap on the cog or ellipsis to access your Options.
   • Scroll down until you see "Clear Search History" and tap on it.
   • Accept the risk by tapping "Yes, I'm sure" [2].

2. Hide the account from search suggestions:

   • In the search tab, tap on the search bar.
   • Tap and hold the name you want to hide.
   • Tap on "Hide" to remove the account from search suggestions [3].

Please note that hiding an account from search suggestions does not guarantee that it will never appear again. If you still follow the account, it may still show up as a suggestion. To ensure it doesn't appear, you may need to unfollow the account directly from their profile page [2].

Learn more:

1. How to hide a name not to appear on Instagram when I search it
2. Instagram 101: Clear Your Search History So You Never See Your Ex's Suggested User Face Again " Smartphones :: Gadget Hacks
3. How to hide who you're stalking on Instagram | Mashable