Like the Doctor, the renegade Time Lord known as the Master used many aliases. However, while the Doctor used false names on a fairly ad hoc basis to avoid awkward questions, the Master usually adopted them in order to further whatever scheme they were embarked upon at the time.
Dr. Aloysius Fischer was the person the Master assumed the identity of, though he assures the Doctor that Fischer is still alive. Aloysius is originally derived from the German name Chlodovech, meaning famous in war.
The Old English word for knife is seax, which is what the name Saxon originated from. His name, then, is ostensibly "Mr. Saxon" - the name given the first time the Saxon incarnation is mentioned in The Christmas Invasion.
While posing as "O", the Master claimed he was named as such as a joke; whenever "O" met with C, C would exclaim "Oh, God!" After revealing himself, however, he explained that he chose the name for satisfaction, anticipating correctly that the Thirteenth Doctor would exclaim "Oh..." as he dropped the act.
In the previews of Ascension of the Cybermen, the Master's return for the cliffhanger was foreshadowed by "Barack Stemis" being credited for a character called "Fakout" at the end of the cast-list. "Barak Stemis" is an anagram of "Master is back", while "Fakout" sounds like "fake-out".
Professor Stream in The Hollows of Time was originally intended to be a pseudonym of the Master, but copyright restrictions prevented them from making this explicit in the story. "Stream", like "Tremas", is an acronym of "Master". The story is listed as a Master one on the Big Finish website.