Setting the SSIDs the same should work and you can even do that for 2.4 and 5g bands. Then the iDevices will connect to the better channel (actually preferred from Apple and a former Apple engineer wrote an article about this). Anyway that works flawless for me on a single router with 2.4 & 5ghz bands. Your issue is caused by iCloud keychain most likely as mentioned. Turn it off and it should solve this particular issue.
The main modem and extender is not a single unit, they are two separate units. But yes I did what they and you said by making the SSID's on the main 2.4 GHz modem and 5GHz extender the same. It actually made the problem worse because unless the iPhone and iPad were in the same room the iPad would switch to whatever wifi the iPhone was hooked to and the iPad was still slow as or or wouldn't work period and I had no way to switch it to the stronger l5G signal. As soon as put the modem and extenders SSID back to factory setting and hooked the iPad back up to 5G it works like a hot dam. I have the iPad set to forget the main modems wifi but as soon as I hook the iPhone up to it the iPad also hooks to it. Which it shouldn't. All I need is to find a way to stop the iPad from hooking up to a certain wifi network. Apple needs to figure that out as I don't want the iPad from hooking up to the regular modem. I don't think that is to much to ask.
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