How is the best way to change the label of an icon placed on the homescreen

I do not see any built-in way to do this.

You can name a bookmark anything you like, but when you long-press a site on the home screen and choose Edit, bookmarks are not always suggested as matches. The only way I can guarantee that a bookmarked site is listed is to add some unique characters to the bookmark name that won't come up in history for that site. Of course, this takes away from having full control...