Source: @GappsLeaks
This feature is still a work in progress though and not yet active unless some flags are changed in the app. The public version of Google Contacts still requires you to open an individual contact and set a specified ringtone for that person or company. Once this feature is finalized though, you will be able to manage all contact ringtones from the “Fix & manage > Ringtones” menu within the app and have all contacts you have set a personalized ringtone for listed in one handy place.
Part of the improvements announced yesterday included the introduction of “Profiles” that tie into the Contacts app and allows users to personalize the profile name and picture associated with their phone number. This will help users set up an identity across Google services that can be saved within the Contacts application and be tied to your phone number in those group chats.