Error Connecting an AirTag

Started pairing a new AirTag and got to the second screen and decided to change the name, so hit back, and this took me back into the Bluetooth settings screen of my iPhone, rather than to the first page of the AirTag setup. AirTag nowhere to be found on my phone. Checked in Find My, and it’s not there. Tried doing the reset procedure by removing the battery, etc., but the tone never changes after 5 battery removal and presses, and it never shows up as a new AirTag in Bluetooth settings. How do I fix this???