No, the address bar keeps showing the real site the whole time. Docognito disguises the page itself, the tab title and the favicon, and it leaves the URL alone on purpose, because rewriting it breaks the assistant. Share a single tab rather than your whole screen and the address bar never travels.
What actually changes and what does not
Three things change the moment the disguise is on. The page becomes a document editor, the tab title stops saying ChatGPT or Claude, and the favicon becomes a plain document icon. Those are the three surfaces a person's eyes land on when they walk past a desk.
The address bar is not one of them. It sits in the browser's own chrome, above the page, and it keeps reading the real address for as long as the tab is open. The extension runs on claude.ai, chatgpt.com and chat.openai.com, and no other website.
| Surface | Disguised | Where it lives |
|---|---|---|
| The page you are looking at | Yes | Inside the tab |
| The tab title | Yes | Browser chrome, rewritten by the extension |
| The tab icon | Yes | Browser chrome, rewritten by the extension |
| The address bar | No | Browser chrome, deliberately untouched |
| Browser history | No | Your profile, on disk |
The row that matters is the fourth one. Everything above it is handled and everything below it was never in scope.
It helps to think about where each surface actually lives. The page belongs to the site, which means an extension running inside that page can rewrite it freely. The tab title and the favicon are odd cases: they are drawn by the browser, but the page declares what they should say, so an extension that changes the declaration changes what the browser draws. The address bar takes its value from nothing the page controls. It reports where the browser genuinely is, which is the entire reason it can be trusted, and that trustworthiness is exactly what stops any extension rewriting it convincingly.
Why the URL is left alone on purpose
This is not an oversight, and it is not a feature waiting to be built. It was built, it shipped, and it was removed.
Rewriting the path meant replacing something like /chat/a1b2c3 with a
document-looking address. Both assistants read their own path to work out which
conversation you are in and where to send your next message. With a false path
in place the composer stopped mounting and messages failed to send. The
disguise looked convincing and the product underneath it did not work.
An extension can never change the domain, only the path
Even a working path rewrite would have left chatgpt.com or claude.ai sitting
in front of the slash. The domain is the part that gives you away, and no
extension can touch it. That is a limit of the browser, not of any particular tool.
So the trade was a cosmetic gain against a broken product, and the honest version won.
There is a second reason to leave it alone, which matters more over time. A disguise that hides the page but leaves a truthful address bar is a tool with a clearly stated limit. A disguise that rewrote the path would invite the belief that the whole address was fake, and somebody would eventually rely on that belief in a situation where it mattered. A limit you know about can be worked around. A limit you have been encouraged to forget cannot.
What this means for a glance versus a stare
Most of the risk this product addresses is a glance. Somebody walks behind you, their eyes cross your screen for a second, and they register a shape. A document shape reads as a document.
A stare is a different test. Anyone who deliberately reads your address bar learns which site you are on, and there is nothing on your screen that will stop them. If your threat model is a person standing behind you reading your browser carefully, no CSS disguise is the answer to it.
Two other things survive a careful look, and both are worth knowing before you rely on any of this. The extension icon sits in your Chrome toolbar like every other extension, though Chrome lets you tuck it into the overflow menu. And the page source, which anyone opening developer tools can read, which is only relevant if the person looking is willing to open developer tools on your machine, at which point the disguise is the smallest of your problems.
In practice the distinction is about attention rather than technology. Somebody walking to the printer is not auditing your browser. Somebody who has pulled up a chair beside you is, and no visual change addresses that.
How to keep the address bar out of a screen share
This is the one situation where you have direct control, and it costs nothing.
Share a tab, not a screen
In Zoom, Teams and Google Meet, choosing a single browser tab sends only the page content. The address bar, your tab strip and your bookmarks never enter the stream.
Check before you present, not after
Turn the disguise on before you click share. Toggling mid-call is visible to everyone watching, which defeats the point.
Remember what a recording keeps
If the call is recorded and you shared your whole screen, the address bar is in that recording permanently, and people who were not on the call will watch it.
The address bar needs a fix of its own
The disguise stops the page, the tab title and the icon from announcing an AI assistant. If you need the address bar hidden too, share a single tab rather than your whole screen, because that is the only reliable way to keep browser chrome out of view. No extension will do it for you.
Use Docognito for the first job, and tab-level sharing for the second.