Times Square is named after the New York Times. It was originally called Longacre Square until the Times moved there in 1904.

Originally known as Long Acre (also Longacre) Square after London’s carriage district, Times Square served as the early site for William H. Vanderbilt’s American Horse Exchange. In the late 1880s, Long Acre Square consisted of a large open space surrounded by drab apartments. Soon, however, the neighborhood began to change. Electricity, in the form of theater advertisements and street lights, transformed public space into a safer, more inviting environment. Likewise, the construction of New York’s first rapid transit system, the Interborough Rapid Transit Company (IRT), gave New Yorkers unprecedented mobility in the city.

In 1905, The New York Times built and moved into the second tallest building, the then-Times Tower, located between Broadway and Seventh Avenue and 42nd and 43rd Streets. It was during this big transition that what was known as Longacre Square, famous for its horse trades, was renamed as Times Square. It was also during these early 1900s that street lamps powered by electricity and electric signs started to appear in the area.

More Info: en.wikipedia.org