Byron names his long satirical poem "Don Juan" to represent its title character. He takes the satire even farther when he insists that readers pronounce the second word as "Joo-an" instead of the Spanish "wuan." Byron does this to make fun of the cultural prejudice that English people had for all things non-English back in the day. He points out the absurdity of insisting that English things are "good" by making the name "Juan" sound ridiculous.
Readers during Byron's time would have been familiar with the character Don Juan from earlier works like Molière's 1665 play Dom Juan. In earlier versions, Don Juan is a middle-aged man who runs around seducing women. Byron messes with our gender expectations by making Juan young and making him the passive object of women's sexual advances. This reversal is all part of his larger effort to turn European culture on its head by using satire.