You can find a conversation or a specific message across everything you are part of.
On the Chats page, click the magnifying-glass icon (Search Chats) at the top of the chat list. Type at least two characters into "Search through your chats...".
Results appear in two groups, Chats and Messages, each with a Show more option if there is a lot. Click a result under Chats to open that conversation, or a result under Messages to jump straight to that message with the matching words highlighted.
On the web, search looks through both conversation names and the message text inside them. On mobile, use Search Chats to find conversations. If nothing matches, you will see "No chats or messages match your search."