Two router setup, one main, one extension via ethernet

The problem is, I can never tell to which router I am connecting

Open AirPort Utility on your Mac and click on the AirPort Extreme and a smaller window will appear.

Look for Wireless Clients

WiFi devices that are connected to the AirPort Extreme will be listed here

Do the same thing for the Time Capsule

If you have AirPort Utility installed on your iPhone or iPad, you can do the same thing on the iOS device.

Question: can the wireless network name be different between the two so that one can tell which router is one connected to?

Sure, but you won't have an extended network if this is the case. You will have two different wireless networks requiring that you log off of one and log onto the other when you want to change networks. A hassle for most users who are moving their WiFi devices around, but perhaps not for you.

If you have a Mac laptop, you can easily check to see which AirPort the Mac is connected to at the moment without using AirPort Utility, but this won't work on an iPhone or iPad.

Post back for more info if you are interested.