What were the names of Sherlock Holmes' parents?

There is a whole area devoted to theories about this which is called Holmesian Speculation.

http://bakerstreet.wikia.com/wiki/Holmesian_Speculation

However, it is speculation; the most likely answer is that they were called Mr & Mrs Holmes - although even that is not certain.

His parents are not mentioned in the stories, although Holmes mentions that his ancestors were "country squires". In "The Adventure of the Greek Interpreter", he claims that his great-uncle was French artist Horace Vernet.
Holmes's brother Mycroft, seven years his senior, is a government official who appears in "The Adventure of the Greek Interpreter", "The Final Problem" and "The Adventure of the Bruce-Partington Plans" and is mentioned in "The Adventure of the Empty House".
(wiki) https://en.wikipedia.org/wiki/Sherlock_Holmes