Why does such a little image always cause so much angst. Changing the favicon should have been added to the to the SharePoint UI by 2013, but in Microsoft's infinite wisdom they have it buried within the darkness of the .master version of the master page. Though, I digress.
Through Designer open the .master of the active master page. Under the following piece of code:
<SharePoint:AjaxDelta id="DeltaSPWebPartManager" runat="server">Add
<WebPartPages:SPWebPartManager runat="server">
</WebPartPages:SPWebPartManager>
</SharePoint:AjaxDelta>
<SharePoint:SPShortcutIcon runat="server" IconUrl="/sites/mySiteTitle/Style Library/Images/Favicon.png"/>Add the image to the Style Library, I added it to the Images folder I created within. (See the IconUrl path above.) Do not forget to save and publish if necessary so all can enjoy. For those that had the previous image cached it may take them a little while to realize the change.