No, they never "switched names." The Chevrolet Suburban has been in constant production since 1935. Even during WWII they built what they called the "Suburban Carryall"
However, you are correct that other vehicles have been called the "Suburban." That's because from the 1930's through the 1960's "Suburban" was not a registered trademark and was a generic term for a specific TYPE of vehicle. Basically, "Suburban" or "Suburban Carryall" were alternative names for the more common "Station Wagon."
It wasn't until 1988 that GM registered the trademark for the name "Suburban."
https://www.caranddriver.com/news/a18356957/the-social-history-of-the-chevrolet-suburban/
If you think about it, "Suburban" is a much more accurate name for a wagon since that's where most wagons were intended to be used, in the Suburbs.
By contrast, the term "station wagon" is a very old term that goes back to the days when long-distance travel was normally done by train. The big hotels would buy specially made vehicles with lots of seats and cargo capacity to pick up guests at the railroad station and transport them to the hotels - which is why they were called "Station Wagons" in the first place.
The term "Power Wagon" was first used by Dodge in the years after WWII. Dodge was introducing a 4wd truck to consumers (the first ones in the country to do so) and wanted to give it a unique name so they chose "Power Wagon", taken from the name of a trucking magazine of the time.
The Power Wagon was not made for the military, it was made for the civilian market but was based on the trucks Dodge made during WWII. In 1951, when the Army wanted a new 3/4 ton truck, Dodge applied many of the design features from the Civilian Power Wagon into the new M-37 series of trucks, and as a result, these are often referred to (erroneously) as "Power Wagons." But the Power Wagon name was always a civilian truck, the military trucks had military designations (M-37 for the pickup, M-43 for the ambulance, etc.) Many of the parts are interchangeable as well since the M-37 series used the same engine, transmission, drivetrain and axles as the Power Wagon.
Originally the term "Power Wagon" only applied to the 1-ton 4wd truck. It wasn't extended to the 3/4 and 1/2 ton trucks until the late 1950's or early 60's.
IIRC the "Power Wagon" name was dropped in the early 1980's when Dodge was trying to reinvent itself with the "RAM TOUGH" image. The Power Wagon became the "Power Ram" for several years. I don't think they resurrected the "Power Wagon" model name until the early 2000's so there was at least a 15 year period when no "Power Wagon" was made.
