get a fake moustache is maybe a way
if you look at it from a statistical view (what all those big companies are doing) and assuming the most people around you are using google or amazon services actively, its not a hard way to profile that its you
if such a big company really have the possibility to identify random people via ring cameras, it could be at some time with high confidence linked to you (in your case to a profile, with an ?unknown? identity) because you obviously dont provide your data actively from other sources (like amazon apps, alexa or what else they have idk) like others are doing around you
but thats only possible, maybe its a way harder to do it in reality