DESCRIBE THE ISSUE IN DETAIL:
AGP failed during syncing project, where there is composite build (includeBuild) of project with, in order, another composite build (i.e. nested composite build).

STEPS TO REPRODUCE:

Create android application project "root/app", and two android library projects: "root/lib1" and "root/lib2"
In "root/app/settings.gradle.kts" includeBuild("../lib1")
In "root/lib1/settings.gradle.kts" includeBuild("../lib2")
sync project app failed with error "Failed to get Gradle name for :"

Full example is attached.

Studio Build: Android Studio Giraffe | 2022.3.1 Canary 11 (Build #AI-223.8836.35.2231.9848316, built on March 30, 2023)
Version of Gradle Plugin: 8.1.0-alpha11
Version of Gradle: 8.0
Version of Java: JetBrains Runtime version 17.0.6
OS: Windows 11

The cause of problem is in com.android.build.gradle.internal.ide.v2.ModelBuilder.
Look into method getBuildName(). There is condition

it.projectDir == currentGradle.rootProject.projectDir

According to Gradle docs, nested composite build structure is flattened, i.e. all the included (and syb-included) projects have same root. See Gradle updated docs in https://github.com/gradle/gradle/pull/24469/files#diff-07fc669ece55f938ee36f360129142a0576f95381ffe9c7f737ce6fe69499993

So when executing on sub-included project (lib2) the condition above will be false, because
parentGradle will be app instead of lib1
parentGradle.includedBuilds will be lib1 instead of lib2
As a result, it.projectDir === lib1, when currentGradle.rootProject.projectDir === lib2

So it is needed to fix getBuildName to solve the problem.