Apple used to make it easier to reset favicons in desktop Safari, but recent versions no longer have a specific item designed for this purpose. You've got two options. You can delete the icon. Free Safari icons! Download 104 vector icons and icon kits.Available in PNG, ICO or ICNS icons for Mac for free use. The wee little icon that appears for most websites in Safari tabs when you have Safari Preferences Tabs Show Website Icons in Tabs enabled is called a favicon.These micro-badges can help you.
Safari User Guide
You can remove all records that Safari keeps of where you've browsed during a period of time you choose. If your Mac and your other devices have Safari turned on in iCloud preferences, your browsing history is removed from all of them. Clearing your browsing history in Safari doesn't clear any browsing histories kept independently by websites you visited.
In the Safari app on your Mac, choose History > Clear History, then click the pop-up menu.
Choose how far back you want your browsing history cleared.
When you clear your history, Safari removes data it saves as a result of your browsing, including:
Apple Safari Icon
Safari Icon Macbook Pro
History of webpages you visited
The back and forward list for open webpages
Frequently visited site list
Recent searches
Icons for webpages
Snapshots saved for open webpages
List of items you downloaded (downloaded files aren't removed)
Websites added for Quick Website Search
Websites that asked to use your location
Websites that asked to send you notifications