How to pin conversations in the Messages application
A new tutorial is available on the Apple support channel on YouTube showing how to pin a conversation on an iPhone, iPad and iPod touch with iOS 14 or iPadOS 14.
In the iOS 14 or iPadOS 14 Messages app you can pin up to nine different conversations. To do this, move the selected one in the list view to the right and tap on the pin icon. You can also hold your finger on it and then move it to the top.