Who are some famous fashion designers from the 20th century?

Armani was a famous fashion designer in this century.

Here's another, better answer:

There's lots of famous fashion designers from the 20th century. Yes, Giorgio Armani was a big one and he still is. But don't forget about Jean Paul Gaultier, who is famous for his avant-garde designs. Also, Hubert de Givenchy, who is especially famous for creating lots of dresses for Audrey Hepburn. Yves Saint Laurent, Christian Lacroix, and Mary Quant (created the mini skirt) were also huge. NEVER forget about Gabrielle "Coco" Chanel, I hope you know who she is.

Hope I could help. :)