Cobb : spider, hence cobweb, also the character from Christopher Nolan’s first film, Following, is named Cobb and was a thief.
Arthur : Arthur Schopenhauer who has said that the spatio-temporal world is the world of our own reflection. Life is like a dream.
Ariadne : the mistress of the labrynth, a weaver.
Eames : first draft probably had him named Dr. Eams (but a variant of Edmund : rich protector). Sam Adams, a critic at Salon offers more : Eames is “a tribute to the American designers Charles and Ray Eames. Although they are probably best remembered for their iconic furniture designs, Charles began as an architect, and the couple made over a hundred short films together.”
Saito : the word for website in Japanese.
Yusuf : Arabic for Joseph the Dream Interpreter from the Bible.
Mal : French for evil.
Robert Fischer Jr : Phishing is to fraudulently attain confidential information over the internet under false pretenses. Commenter Hollie adds that Bobby Fisher is also the name of chess genius. Robert connects to the next character as well.
Browning : Robert Browning, a poet who wrote a series of poems title Bad Dreams. Also : “At last awake / From life, that insane dream we take / For waking now.”