Logo Picker for Twitter
You can open the logo dropdown by hovering over the logo in the top left and click the little down arrow.
You can also open it by pressing Q .
By default, the logo dropdown only shows logos that were used by Twitter at one point.
To see more logo choices, press the Shift key while opening the dropdown.
Rebranding
With each logo comes a set of alternatives for Twitter-branded terms.
For example, with this logo
(Credits: idea, art), "Twitter" becomes "Pigeon", "Tweets" become "Coos" and "Retweets" become "Grunts."

In the off chance this is just too much for you, this can be disabled in your Userscript extension's command menu.
Logos available
The default logo dropdown has 4 logos available:
 | The dreaded X. | Branding: X, eXecrate, ReeXecrate. |
 | The blue bird. | Branding: Twitter, Tweet, Retweet. (default logo) |
 | Old blue bird. | Branding: Twitter, Tweet, Retweet. |
 | Older blue bird. | Branding: Twitter, Tweet, Retweet. |
If you opened the dropdown with Shift + Q or Shift + Click, the additional logos are available:
 | Bouncing Pigeon | Branding: Pigeon, Coo, Grunt. |
 | Bluesky | Branding: Bluesky, Skeet, Reskeet. |
 | Threads | Branding: Threads, Post, Repost. |
 | Mastodon | Branding: Mastodon, Toot, Retoot. |
 | Parler | Branding: Parler, Twat, Echo. |
 | Truth Social | Branding: Truth Social, Truth, ReTruth. |
 | Reddit | Branding: Reddit, Spez, Respez. |
Favicons
Every logo comes with a matching favicon that is shown in the browser tab.
Everywhere
This script could have just updated the top left logo and called it done, like dozens of others have.
But it didn't. It kept going.
This is what you'll see if you open twitter while logged out:

This is what about.twitter.com looks like:

So on and so forth.
All At Once
Your logo and branding selections are synced across all your tabs instantly.
The logo dropdown may only be available in the twitter app itself, but you will see its effect immediately in any other twitter.com page.