I have not even seen it in 40+ years, but there was one near Charlotte in Kannapolis, NC (or was it Concord?) when I was growing up.
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Those were not a part of the Texas What-A-Burger chain.
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What-A-Burger restaurants (as well with other variations of the name) were formed by other entrepreneurs than the Branch family during the post-World War II period. For example, a small chain now based in Concord, North Carolina, was founded by Eb Bost & C.W. Bost, Jr. and operates as What-A-Burger Drive-Ins, Inc. with several locations, are all still under the leadership of members of their families.[1] It also visibly numbered their stores starting from #1 in Kannapolis, North Carolina to #15 in Concord.[2][3]
The What-A-Burger restaurants in Virginia, North Carolina and South Carolina are not to be confused with the much larger Whataburger chain based in Texas.
https://en.wikipedia.org/wiki/What-A-Burger
There was a small burger chain (Mom and Pop, really) here in San Antonio many years ago called Whopper Burger.
And when Burger King (home of the Whopper) finally got to Texas in the 1980’s they had to allow this chain to continue on with Whopper Burgers. I can’t remember if there were any legal issues, but Whopper Burgers finally closed or were bought out when the owners retired.