As an alternative to @peterh's solution you can go to whatever device "manages" your Alexa devices (computer, tablet or phone), go to wi-fi/connections under the SETTINGS menu and look for your new wifi service name and click to connect then click to enter that devices passcode (usually on the box or the wifi service letter.
NOTE: If you have one device only I think my suggestion is quite easy and fast. If you have more than one device then I STRONGLY recommend @peter's solution - otherwise you will have to find/forget/connect/verify on every darn device! (Just been daft enough to do this on 5 Fires, 2 Kindles, 1 iPad and an alarming number of phones. Took ages!)
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I wonder why someone would follow their own alternative forum profile.