Reproduction steps:
1. Create a new project
2. Right-click on any GameObject and select Properties to open a Focused Inspector window
3. Change the name of the GameObject, either from the Scene Hierarchy or from the Focused Inspector itself

Expected result: The title of the Focused Inspector window tab is updated
Actual result: The title of the Focused Inspector window tab stays the same

Reproducible with: 2020.1.13f1, 2020.2.0b11, 2021.1.0a5
Could not test with: 2018.4, 2019.4 (No Focused Inspector window)

Note: tested with 2021.1.0a7.1331. In that version of Unity changing the name from Hierarchy would update the Title properly. But changing the name from the Focused inspector won't update the title.