@j99lemmon,

Most likely, you are correct, and you want them to be separate networks that your phone will switch between. Your second range extender was simply extending your main Wi-Fi(as it should). so it never saw your Range Extender on the network - which means it simply chose its default network name again.

You are, however, beginning to see the advantages of EasyMesh or other Mesh technologies, as it allows for one coherent network.