I just got a new phone yesterday and was experiencing the same issue. I spoke with Apple support, who were able to help me resolve it. At first they asked me to reset the air tag by removing and replacing the battery 4-6 times (without replacing the cover each time) until I heard a different sound. That did not resolve the issue on its own, and I am unsure if it was necessary at all. They then asked me to reset my network settings (this did the trick). Go to Settings, General, Transfer or Reset iPhone, Reset, Reset Network Settings (be careful not to hit any other option here). It then asked me for my phone passcode, and then required me to confirm that I wanted to Reset Network Settings. I was told by Support that our phone call will disconnect, and that she would call back (which she did). She also told me that I would need to re-enter my wifi password to reconnect to my home wifi. This too was accurate. After all this, my phone automatically recognized my nearby airtag and allowed me to reconnect it and custom name it. After doing so, I noticed that all 4 of my airtags were then visible on FindMy under Items, without further steps. Woohoo! If you hit a snag, search your phone for the Apple Support app and request to be called. The response time was reasonable and they were able to resolve this issue. Good luck to you.