For instance, if I say “What is the capital of Burkina Faso”? Please answer and do not google (or Google) the answer. Well that’s actually a bad example 'cause everyone knows the capital of Burkina Faso is Ouagadougou.
And before anyone says “You shouldn’t be using Google as a verb” well even if that was true, people still do it.
I’m not sure of the answer to the OP, but that is not a good example. Yes boycott is derived from Charles Boycott, but the noun is no longer used to refer to that particular person, and so even as a noun it is not capitalized.
The verb “boycott” was not capitalized even when Boycott was around.
And there are plenty of additional examples: orient, taser, mimeograph, videotape, yo-yo, zipper, photoshop, etc.
Verbs are just not capitalized, except at the beginning of the sentence or in other odd cases when standard rules of grammar require it (e.g., in titles). If a proper noun becomes a verb, it loses capitalization.
Burking was sort of another proper noun to verb. William Burke and William Hare used to get their victim drunk and sit on their chest to asphyxiate them. It is referred to as burking from Mr Burke
Other examples are lynch, from William Lynch, gerrymander, from Elbridge Gerry, *bowdlerize, * from Thomas Bowdler, and guillotine, from Joseph Guillotin.