Is it feasible for hackers sitting near you to have some sort of RF listening device that uses your phone's transmissions to identify your name or other information that could be used to determine who you are? Would this be through the network, wifi, and/or bluetooth? If so, are there any protective measures that people can take that don't involve simply turning off transmissions?
AS Hugo stated, yes the phone can act as a tracker via it's IMEI & SIM card IMSI numbers. These are sufficient for a telco to identify the phone owner, but a third party can still identify the unique phone without necessarily knowing the registered owner. Even without actively using the phone, it pings towers to let the network know where you are in order to handle call routing for you.
Additionally with many modern smart phones, turning it off doesn't really turn it off, you need to physically remove the battery to make sure it's actually off. This can be problematic with many phones (Apple).
Putting the phone into "airplane mode" will stop it from talking to cellular towers. Unfortunately many smart apps collect WiFi SSIDs that they've seen and will report that information later after you come back online, providing an historic trail of electronic bread crumbs.
Faraday bags and such will only make your phone spike its power levels to punch through, rapidly killing the battery in the process.
Your phone could be used as a tracking device. If you have bluetooth or wifi on, "someone" could track you around using the unique numbers those interfaces provide.
Even now, with some fake cellular towers they can track your unique number signaling from the phone.
From that to reveal your true identity is a little more complicated. They should intercept your communications to extract valuable information, like email, not only the unique numbers to track you.
So, you should turn off your phone to not been tracked.