Formula 1 teams aren't as straightforward as you think. Some teams, like Ferrari, Williams, and McLaren, have been around forever, and were always owned by the same entity. Pretty much every other team, though, has changed hands (and names) several times throughout their histories.
The WTF1 YouTube channel was nice enough to put together a brief history of every team currently entered in Formula 1. Perhaps the strangest team is Renault, which started out as Toleman in 1981 before turning into Benetton in 1985. By 2002, Renault purchased the team, and in 2010, it became Lotus-Renault GP (though the team's official constructor name was still just Renault). In 2012, the constructor name changed to Lotus, but a new Malaysian team entered the sport and called themselves Team Lotus, which ran at the same time. Neither of these teams, by the way, had any relation the original Lotus that competed in the 1960s. By 2015, the Renault name returned, and that's how it remains today.
Another interesting one is Mercedes. The team known as Mercedes started as Tyrrell in 1971, before evolving into BAR in 1999. In 2006, Honda took over the team before leaving the sport in 2008, allowing the Brawn GP to form in 2009. At the end of that year, Mercedes bought the team. That means Mercedes was once Honda.
Those are just two of the 11 teams histories, though. Check out full video here to learn more.