Is there an existing issue for this?

• I have searched the existing issues
• I have read the guide to filing a bug

Use case

Sometimes when troubleshooting issues with your Android installation, it is handy to know which version of Android Studio you have installed. Personally I first think about the monicker that comes with the version (i.e. Electric Eel or Flamingo)
when asking someone else what version they have installed. Just because I don't know what version number is which installation exactly.

However flutter doctor (-v) only prints the version number of Android Studio (i.e. 2022.2).

Example:

flutter doctor

[✓] Android Studio (version 2022.2)

flutter doctor -v

[✓] Android Studio (version 2022.2)
    • Android Studio at /Applications/Android Studio.app/Contents
    • Flutter plugin can be installed from:
      🔨 https://plugins.jetbrains.com/plugin/9212-flutter
    • Dart plugin can be installed from:
      🔨 https://plugins.jetbrains.com/plugin/6351-dart
    • Java version OpenJDK Runtime Environment (build
      17.0.6+0-17.0.6b802.4-9586694)

Proposal

Add the monicker that comes with Android Studio releases (if any) to the output of flutter doctor.

(with monicker) Android Studio Flamingo (version 2022.2)
(without monicker, as it is today) Android Studio (version 2022.2)

@andrewkolos Do we also need a list of monickers in the output?