It's not possible, specifically there is no way to fetch the window name (as mentioned by the feature request) whatsoever. The closest is with the ID that chrome.window generates for each tab, however you cannot use this as a way of mapping it as it is unique per session, meaning when the browser is closed, it will generate a new ID, and the ID itself has no inherit information in relation to what the window name is.
An actual implementation would need to be done outside the extension itself, e.g.:
e.g: import pygetwindow as gw
# Get a list of all Chrome windows
chrome_windows = gw.getWindowsWithTitle('Chrome')
# Print the title of each window
for window in chrome_windows:
print(window.title)
which is a hacky, but only real viable way to get the name until it's implemented in the API.
Cheers,
Deco