How do I change the Home Page icon of Safari on Mac?

Ok thanks. Two solutions come to mind; one is to delete the Safari favicon cache which you can do with its Develop menu: Develop menu | Apple Developer Documentation. Quit Safari and the icons will repopulate on their own upon the subsequent launch.

The image source (if any) is coded in webpages though. If you want to change the favicons to reflect your own customized ones, their images can be found in the ~/Library/Safari/Touch Icons Cache/Images folder. However, I do not know if merely changing those images will cause the favicon database to reflect those changes.

I have never been terribly interested in favicons though, and I never looked into altering them, so I'm not the one to ask. It seems to me those webpages will override any changes you make, assuming of course the webpage contains those favicon images (they're optional).

Your question is not quite clear to me.

Customize a start page in Safari on Mac - Apple Support