As already mentioned, the company did something similar with Hangouts Meet, as it changed its name to Google Meet. It seems like Google is completely phasing out the 'Hangouts' brand.
Hangouts phase-out continues, Hangouts Chat becomes Google Chat
The information regarding Hangouts chat to Google Chat rebranding has been shared by The Verge, and confirmed by Google. Google's spokesperson confirmed that "there will be no changes to the consumer (classic) version of Hangouts".
That version is going away completely, but the company will not change its branding before then. This change applies only to the G Suite version of the service, called Hangouts Chat, not to be confused with the regular 'Hangouts' app which is available in the Play Store.
These changes are not surprising at all. Google Hangouts never managed to become the messaging platform Google wanted. That is actually the company's own fault, at least partially.
The Hangouts app was competing with a ton of other similar apps from the same company. Google's strategy regarding Hangouts was never exactly great, so it didn't really reach its potential in all these years.
Hangouts / Google Chat, unlike the regular Hangouts app, is more of a Slack competitor, than a competitor to messaging apps. It's a workplace productivity and messaging tool, which is why it's a part of G Suite.
Regular Hangouts app was supposed to shut down in August, but…
We still do not know when will the regular Hangouts app go away. It was supposed to be shut down in August this year, but Google postponed its demise. So we're waiting for more information.
The company actually released an update for Hangouts a month or two ago, though it did not add any new features, but removed one. Hangouts will no longer be getting new features, or anything of the sort.
We're expecting the service to be completely gone in that form by the end of the year. Google Chat and Meet should replace it, along with Google's Messages application which has RCS support in some regions.
Google is planning to push its Messages app forward, and use that as a competitor to Viber, WhatsApp, Facebook Messenger, and so forth. If RCS actually becomes a thing, that app has a head start.
That is more or less it. Google is slowly but surely phasing out the Hangouts brand. Soon, that name / service will be a distant memory, like many other services from the company.