Is there such a thing as a wifi proxy?

Hi.   I work for a large entertainment company.   I am programming skills for Alexas.   Echo Show devices.   "Alexas" are no longer just black cylinders.   Now, some of them have screens. 

My problem is that some of my testing has to be done with Echo Shows in locked-down mode.   I can't change the wifi connection in locked-down mode.   I have to put the Echo Show into non-locked-down mode (difficult to do), establish a connection to a wifi, and then put it back into locked-down mode.   The Echo remembers the wifi when it goes into locked-down mode. 

So, last week we had a hurricane.   I had to work from home.   My Echo didn't know my home wifi.   Shuffling through a bunch of devices, I finally found one that would recognize my home wifi. 

When I got back to work, that device wouldn't recognize my work wifi.   Arghh. 

Today, I had to make an emergency stop at an auto mechanics.   I could work, they have a comfortable waiting room, but I can't make any of my devices connect to their wifi. 

Is there such a thing as a "wifi proxy?"   It connects to some wifi on one side, whether the mechanic's wifi, my home wifi, or my work wifi.   On the other side, it always presents "itself," so I can set my Echos once, and reliably use them anywhere. 

At work, it is difficult to find a working cable connection.   At the auto mechanic's, too. 

Is it clear what I am trying to find?   Does that device exist? 

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I talked to some people, and I learned a little more.   Netgear's "mesh" solution is not appropriate for me.   I want the network name that my device sees to be the same, as my wifi proxy device goes from network to network. 

It seems clear that I want what Netgear calls a wifi extender.   But I am lost in the large collection of devices that Netgear sells.   Which one is appropriate for me? 

One worry I have is, how do I set up the wifi extender?   That is, give it the name and password of the wifi it should talk to.   Is there an app?   Do I do it on my phone? 

                    Regards, Rick