How to prevent Gmail from knowing my name?

Question

I care very much about the privacy and always surf the Internet using the private mode of the Firefox. Also, I never let any browser to save my account and password. Theoretically, the web browser or any website should have no idea about who I am if I do not log into any account.

However, today I noticed that the all-mighty Gmail knows my name even before I logged into it! I remembered that in the good old days, Gmail was asking for the account and the password at the same time when I wanted to sign in. But things are different this morning.

When I opened the Gmail page, it asked me to provide my account only. After I gave it my account, it showed my name on the page correctly and asked me for the password to log me in. Then I came up with a question that "does this mean I can know the name of the owner of any Gmail account through this way?"

So I made two experiments:

1. I tested the Gmail log-in page with some other Gmail accounts but it refused to show me the owner's name of the accounts. (Actually, I am the owner of the tested accounts.)
2. I launched a browser that has been forgotten for a very long time, AKA the legendary IE, to log into Gmail again. Not surprisingly, Gmail cannot recognize me with only my account provided.

Well, it seems that there must be some sort of ways that Gmail links my name, my account, and my Firefox all together, so it feels comfortable to show my name in my Firefox when I am not signed in any Google account. But I thought the private mode of Firefox should guarantee that such thing would not happen to me.

Okay, so here are my questions:

1. How does Gmail link my name with my account when I visit it using Firefox with private browsing?
2. How can I stop it?

Answer 1

This is not an answer, but has further information that may help someone to answer the question.

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I use three profiles regularly on Firefox (v38.0.5) for Linux, and added two new profiles to reproduce the issue OP has.

Scenario 1

1. Created Profile 1, and added no addon/plugin. Default profile from scratch to be precise. (No other profile is running except this one.)
2. Launched Private browsing and opened gmail.com
3. Logged in (two-step verification) with Stay signed in checked. Note that I didn't check Don't ask for codes again on this computer for two-step verification.
4. Relaunched Firefox and repeated step 2.
5. As OP said, as soon as I entered my email ID and clicked Next, Gmail detected my name registered with account.

Scenario 2

1. Created Profile 2, and added no addon/plugin. Default profile from scratch to be precise. (No other profile is running except this one.)
2. Launched Private browsing and opened gmail.com
3. Logged in (two-step verification) without Stay signed in checked. Note that I didn't check Don't ask for codes again on this computer for two-step verification.
4. Relaunched Firefox and repeated step 2.
5. As OP said, as soon as I entered my email ID and clicked Next, Gmail detected my name registered with account.

It must be noted that there is no trace of any browsing history (including Form history) which means I cannot delete or forget any site since they were never visited in default Firefox browsing mode.

Is this some kind of terrible feature of Firefox, a bug, or Google seems to show the name based on User-agent I guess.

Regardless of what it is, how do I get rid of it?

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Update 1: There are two things that I found very interesting. IDT whether Firefox is the reason or the Google itself is doing it, but here it is -- You do not get to see the name in Private browsing if:

• you change the IP address (I use two different carriers)
• you tweak the User-agent to something that makes no sense (like weB.32.x64.ApplicationS) -- in this case, Gmail throws both Email and Password field at once, and doesn't detect the name, no matter what.

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Update 2: Chromium for Linux rather behaved differently here. It reproduced the issue for one IP but not for the other (tried multiple times). I think Google has something to do here.