You may not get a reply, since hat was over 18 months ago, and he hasn’t been active, on the forum, pretty much since then.
No reason why you can’t have a separate name, such as routerext. In my opinion, it’s much preferred. As you said, it’s very hard to tell if you are still clinging on to a weak signal from your main router, or are indeed connected to the extender, unless you have a different name, other than poor signal strength in the app, but if you are, how on earth do you ‘make’ it connect to the nearer extender, unless it has a different name.
Same name may work well for wandering around your house with a laptop, but, in my opinion, it’s not good in this situation, and it certainly didn’t work well for me.
A different name works perfectly, even for my laptop, since I just changed the Wi-Fi settings on the laptop to aggressive switching, or similar name.
Not sure how it couldn’t work, if you pick that name during set-up, and the extender really has got good connectivity to your main router. My extender is cabled to the router, so I know it’s connection is good, and it’s near the sync unit and camera, so I know the Wi-Fi’s good too, together with being able to see the strong signals in the app.