As some other posts noted, it was named the "Library Tower", and is still called that by most. It got the name by acquiring the air rights over the main LA Public Library building across the street (the LA Public Library sold it's rights to expand upward). Los Angeles allows stacking of air rights that allows a building to built higher than the standard maximum height, which is something like 50 stories. By acquiring the air rights over the approx 6 story LA Public Library, the Library Tower was allowed to go up to 72 stories. The LA Public Library used the proceeds of the sale of its air rights to rehabilitate and expand the LA Public Libary after a devastating fire in the 1980s.
Interesting. Thanks. I haven't been to LA since the 70's.