If you wish to change the "brand icon" displayed in the Google search results page (right next to your official website rate for free or paid booking links made available thanks to the Channel Manager), then you should follow the instructions at the link below directly on Google:

https://support.google.com/hotelprices/answer/9919249?hl=en

You basically need to submit to Google the icon you would like to see displayed, which needs to respect the required format. You may also be asked to provide your hotel_id, which is the ID that was assigned to your property by Vik Channel Manager upon configuring the channel Google Hotel. You can find it in the page Settings of Vik Channel Manager when Google Hotel is the active channel. Make sure to provide to Google all the required information beside your hotel_id with e4jConnect.

Once Google will have accepted your request, the logo change should not take longer than 3-5 business days.

The screen shot below shows what's the "brand icon" you can customize for Google: