My right AirPod not charging

Try a full re-pair, reset, and try again.

Settings > Bluetooth > Airpods > Forget this device. Confirm it.

Put both Airpods in their case, charge them via Lightning for a few minutes (or preferably until the case is 100%). Unplug them. Open the case and hold the button on the back of the case for 15+ seconds or until the light flashes white. Hold them near your iPhone and see if the pairing screen comes up and pair them. If not, repeat until it does. But if you can't see the screen pop up, then manually pair within Bluetooth.

If it doesn't work, open a case with Apple Support here: https://support.apple.com/airpods