I tried to choose names that would evoke the eras in which the city would have seen its first wave of pro sports clubs. So, generally, the northern cities will reflect early 20th century origins, California and Texas will be WWII/postwar-era, and the sunbelt cities will be 1970s or beyond.
-I see this team as having origins as Hollywood Stars FC, then switching it up upon moving to Anaheim.
Carolina Vulcans, Carolina Flight, Carolina Aviators, Charlotte Spirit
-The area has a history with racing and, thus, vulcanized rubber. But the Vulcans name can also lend itself to an identity that has nothing to do with racing if you go with that theme for Indianapolis. Flight and Aviators have more to do with the area's Aviation history. Spirit was the original nickname for the NBA team that eventually became the Charlotte Hornets.
-Any monarchy themed name would work here. But this one seems to lend itself more to soccer than any other option.
Cleveland Foresters, Cleveland Lakeshores, Cleveland Shoremen
-I feel like a Cleveland club would have began as Forest City FC or Lakeshore FC and acquired one of these nicknames.
-Many early 20th century teams acquired nicknames based on their colors There's a good chance a Columbus club would have aquired equipment from Ohio State and possibly shared facilities at some point.
Dallas Pegasus FC, Dallas Wingsteeds
-My inspiration came from the Akron Wingfoots basketball team, named for their sponsor's (Goodyear) logo. Mobil Oil is a company I could see sponsoring a soccer team and also has an iconic logo of Pegasus, the mythical winged horse and a civic symbol for the city of Dallas. Pegasus could concievably work for a soccer club the way New York Apollo did in the 1970s. But I feel like Wingsteeds is such a unique name that could have only come from the mid-20th century. If that seems too ambitious, Wings or Pegs could work.
-This was the name of a short-lived minor league hockey team and, as mentioned earlier, has real life history in soccer. You seem to want a space-agey nickname fo Houston, and this works better than Cosmos, which would feel wrong if used anywhere outside of New York.
Racing Indy FC
-I see this team as having 1970s or 1980s origins, shortly before or after the Indianapolis Racers of the WHA. They would have adopted this name befor the WHA club, or after it folded, then rebranded in the mid-2000s when European-style names became en vogue. Fortunately, this one isn't a reach and makes total sense for a place like Indianapolis.
Las Vegas Flash, Las Vegas Atoms
-Las Vegas probably wouldn't have had a team until at least the 1990s and Flash would be a fitting nickname for that era. It would have carried over to now because it would have been the first major pro sports operation in Las Vegas and the fans wouldn't want to divorce themselves from that success. If Miami and Orlando can get by with Heat and Magic, Flash isn't too much of a stretch. It also fits the "odd" category you seem to want for Vegas. Either name lends itself to a cool crest based on the over-the-top "atomic age" road signs from Vegas' heyday.
Miami Internacionales, Miami Flamingos
-Not surprisingly, both are related to the Miami's probable real life soccer brand, and for good reason.
Milwaukee Bocks, Milwaukee Herons, Milwaukee Gulls
-Bocks is a great name if you don't want something too close to Brewers, but still references beer. Plus, it could lend itself to a cool crest based on a goat. If you want to go more the Lake Michigan route, any marine bird native to Wisconsin would work. Herons and Gulls are two that are very common in Milwaukee. The oldest soccer club on record in the city is Milwaukee First Ward, which would have been based in a district near the lake and is something you may want to consider.
Nashville Cumberlands, Nashville Showmen
-Cumberlands sounds more early 20th century, but the backstory could be that it's a tribute to an early soccer club in Nashville called Cumberland FC. Showmen feels more like something that wouldn't have been out of place in the NASL.
Oklahoma 66ers, Route 66 FC, Mother Road FC
-Stampede feels appropriate, but a name based on Route 66 would lend itself to an interesting badge design. Soccer is probably also the only sport where you could base a brand on the famed route's "Mother Road" nickname and get away with it.
Sacramento Solons, Sacramento Rivermen, Sacramento Ursine FC
-Sacramento is a tough one because there's not really anything you free-associate it with other than it's in California and it's the capital. Solons is an old PCL team nickname that could make for an interesting soccer identity. Maybe part of the back story is that some of the old PCL clubs operated soccer teams in the off season. Rivermen is because Sacramento is one of many cities that claims River City as a nickname. Ursine is a bear reference that fits more modern soccer club naming conventions. I see a crest that would involve the Ursa Major constellation, which could be pretty cool.
San Diego Santos
-The Raiders original nickname was the Senors, so it's not exactly a stretch that a team in San Diego would have gone with the Spanish version of "Saints." I do like the possibility of Toros as well.
Utah Swarm, Utah Mountaineers
-Swarm is a nickname born out of the 90s when I could see Salt Lake City acquiring a team, and it references the Beehive State. Mountaineers should be pretty obvious.