Radios take power; batteries.
There is no such thing as a remote accessible implant, small enough to not need major surgery to install it, that could work for more than a few hours.
Something the size of a matchbox could work for a few days with an active receiver.
Think of the size of a cellphone battery and how long one can last on standby without using the screen and with everything possible shut off - a week or two at most, for something with the case half filled by a battery.
Actual surgical implants that communicate continuously, such as a cochlear implant for hearing, use transformer coupling from an external power unit with a part that is placed against the skin over the implant.
They are also quite large and very easily detectable on x-rays - even without a battery.
Invisible / injectable implants that communicate remotely are pure fantasy.
Things like pet ID tags are nothing more than an electronic "bar code" and can only be read from a few inches, again using a powered device with a coupling coil. They are the same basic technology as door entry keyfobs / keycards etc.