I don't really understand your point here. If most users start with 'famous' non-Microsoft browsers, that fame consists of far, far more than a mere logo. Logo recognition, if any, comes
largely after the fame has arrived. Fame, as you call it, is either the result of usage reviews/recommendations regarding the product design/performance or the result of marketing exposure and strategy.
You don't understand because you lack the knowledge of branding, did you check-out the link I sent you, about Google's logo?
I really don't know how I can emphasize on this anymore, logo recognition is not the point. It's not about recognition, it's about the affect. There is a difference. Fame doesn't just arrive to your doorstep just like that, just because it's good, and reviews, it about publicity. And when competition increases, -which is what is going on now,because we have more and more browsers- this is where branding plays its role.
Chrome rose to market dominance largely because of two key factors: the design simply worked with almost all websites without expert user intervention and because of Google's enormous investment in Chrome's marketing/tie-ins/publicity.
Lol, I think you have already accepted the fact that it's about publicity. https://www.garyvaynerchuk.com/how-important-is-a-logo/ please read this. I believe it would change your views and broaden your view about logos and the extent to which it can interfere users and their decisions. It's a post by Gary Vaynerchuk-an American serial entrepreneur, four-time New York Times bestselling author, speaker and internationally recognized internet personality.
They continue using the browser if they remain happy with how it operates, its feature-set, speed, and so on... but it's hard to see how the logo has anything to do with any of that.
I really think it's fool's errand to repeatedly explain to you about the effect logos have on our "minds". I would strongly suggest you to read the link above and also about the history of Google's logo.
This actually makes no sense. You switched to Opera because it has something important to you that Chrome lacks, as many other Opera users have similarly done.
Google Chrome didn't lack anything, I switched just coz I wanted a change. Just a change, change is triggered by?? branding! I hope you have some idea. 
Chrome is number one because its feature set and performance are all that most generic users demand and because it's been powerfully (and expensively) marketed.
It's really funny how you blindly say marketed, Don't you know brand name, logo, etc etc are parts of this procedure. I just feel that an engaging logo, could be a cheap alternate for Opera's marketing strategy. We may not be the lead the market share for obvious reasons-as you mentioned- but there are still people who would change their browser for a good set of performance elements, and this set of people is quite a big share. What's going to help trigger this change? Yes, you've got it. Logo will play its part definitely. Not the part, but definitely "a" significant role.
Alternate browsers like Opera exist by supplying feature or performance elements that Chrome lacks for users to whom those matter. Unless those alternative browser makers commit resources akin to Google, their marketing (and browser adoption rates) will never rival Chrome. And simply changing a logo to enhance branding is a far cry from what would be required.
What's required? I don't know Opera's agendas. That's not the point I am making in this post. And yes, you are very right about "supplying feature or performance elements that Chrome lacks for users to whom those matter"- This is exactly my point, there are yet so many people to whom these performance elements do matter, BUT THEY JUST DON'T SWITCH. WHY? WHY?
WHY? This is where I believe the logo can have a significant influence. Please do not comment on this post without a shade of knowledge in branding and brand images. please.