Can we use different logos for desktop and mobile version website
We have a website and for the desktop version we have designed the new logo with our client numbers on it. For mobile version considering the ux changes we are retaining the old logo. Will it be harmful for my website ?
Not harmful, different images can be used for different devices.

No, it's not advisable. Google suggested that the mobile view should be same as desktop view.
I see your point about maintaining consistency across devices for SEO purposes. It makes sense to keep the branding aligned to avoid confusing users.
However, I've seen some brands successfully use different logos for mobile and desktop to enhance user experience without harming their SEO. It might depend on how significant the changes are. Have you come across any examples where this worked well?