There seems to be 2 logos for New York Yankees. The rightmost one seems to be the official one. How about the leftmost one?
The left logo is the official team logo since 1968.
The right one with the letters NY is the more famous one, because it's way older and they still use it on the caps and jerseys. This iconic logo has been introduced in 1915 and was the official brand logo until 1946 and has been used on the team wear ever since.
In 1947 the Yankees introduced a logo very similar to the left one.