No FAA radio license
There's no FAA issued radio license or test.
In the old days, you'd get a radio transmitter license from the FCC (Federal Communications Commission) which licensed you to use the various transmitters (Com, ELT, TXP) in your aircraft, no license was required to receive. It was $75 for 10 years. If you didn't get the radio license, you could still get a pilot's license but you couldn't use anything that transmitted - so everyone got the radio license.
The FCC (finally) realized that it was costing them more to collect the $75 and file the information than it was worth (parking meter syndrome), and there was really no valid reason to collect it anyway other than "we've always done it this way" so in a moment of sheer genius decided to eliminate the requirement entirely. (Are you listening, governments everywhere????)
You no longer need to get a radio license in the US. (I still have mine, issued in 1979, taped to the inside of my logbook - just for old time's sake.)
If you plan to take your N-reg airplane outside of the United States (even only to Canada, Mexico or the Bahamas), ICAO regs say you are supposed to have this license, so you get to go back to the FCC with $75 in hand . . . and you're good for another 10 years.
The FCC realized they weren't DOING anything for the $75 other than mailing out pieces of paper - no test, no compliance requirement, no field checks, no equipment inspections, just maintaining a database of people who had paid $75 to be allowed to talk on aircraft radios. They drove a stake through their own hearts before the OMB did it for them (Office of Management and Budget - looks for instances of absurd waste in government and actually does something about it, sometimes.)
Best Regards,
Echo Mike