Google is working on a pinned conversations feature for Google Messages6
You might be able to pin your favorite conversations on Google Messages
At the moment, this feature is not available to the public or on a stable build, but XDA-developers have found it hidden in the code for the Google Messages version 8.1.050. Keep in mind that this feature may not make it to the final release, as developers may decide it is not stable enough; however, we find this feature useful for people having loads of messages in the app.
Along with the support for pinned conversations, the possibility to star messages has also been found in the code. The pinned conversation will be visible on top of your conversations list, making it easily accessible once you open the Google Messages app.
Right now, the feature lets you pin up to three conversations; however, Google might decrease or increase the number before the new feature makes its way to the public.
Another feature that could come in a future Google Messages update is the ability to star messages. Starred messages could be easily searched through the app’s search interface.
Keep in mind that these features are not live in the current Google Messages app version and we don’t know when and if they will make it to the public release yet.