Anaheim is not Los Angeles, and it's not in Los Angeles County.
It's an independent city, and it's located in Orange County.
However, in practice, people have a tendency to refer to "Greater Los Angeles", an imprecise term which covers both Orange and L.A. counties - basically the whole megalopolis here. In physical terms, there are no barriers or empty land between the two counties - they run together to form one giant metropolis - the borders only show up on maps and the occasional road sign.
The Angels have always played in Anaheim. They were originally called the California Angels. When Disney bought them, to please the city of Anaheim, he changed the name to the Anaheim Angels.
But when Moreno bought them, he realized he was competing with the Dodgers for essentially the same audience of baseball fans (people from Orange County go to Dodgers games, and people from L.A. County go to Angels games). He thought the name "Anaheim Angels" made the team seem less appealing to the larger L.A. area, so he changed the name to the Los Angeles Angels.
But apparently some clause in the city contract made it essential for him to include the name Anaheim in the team's name, so they wound up with the awkward moniker of "The Los Angeles Angels of Anaheim".