There is more than one artist with this name, including:
1) Teddy and the Rough Riders was an American instrumental group from Fairborn, Ohio (a suburb of Dayton) that was a popular draw in the area during their existence in the years 1957-65;
2) Teddy and the Rough Riders is an American country rock band based in Nashville, TN.

1) Teddy and the Rough Riders was an American instrumental group from Fairborn, Ohio (a suburb of Dayton) that was a popular draw in the area during their existence in the years 1957-65. Originally known as The Teddy Bears, they recorded all of their music at King Studios in Cincinnati, Ohio.

2) Teddy and the Rough Riders is an American country rock band based in Nashville, TN. The band self-released "The Congress of Teddy and The Rough Riders" in 2019.