"Speak, Memory" hasn't been this book's only title, which should tell us something big. In the foreword, Nabokov explains. The first American edition was called "Conclusive Evidence," a tip toward the fact that an autobiography is another way of saying, "Hey, I'm here!" And in Nabokov's separation from his Russian identity, a statement like that makes sense.
Nabokov also lets us know that he wanted to call the British edition Speak, Mnemosyne, alluding to the mother of the Muses (responsible for inspiring artists everywhere) in Greek mythology. Her name is also where the word "mnemonic" comes from: a technique for remembering something, like the famous "Every Good Boy Does Fine" to remember the order of the lines of the treble clef. This book is all about language, learning, and remembering. But his editors said "little old ladies would not want to ask for a book whose title they could not pronounce," and we don't blame them. (Foreword.5) Nabokov settled on the simplified version—"Speak, Memory"—and it stuck.
For the second major edition, when Nabokov and his wife translated the book into Russia, its name became "Drugie Berega," which translates roughly to "Assumed Second," perhaps a clue to the order in which young Vladimir learned his languages, and the fraught Russian identity he'd later try to recover.
In French, it was called "Autres Rivages," or, "Other Shores," a clear allusion to Nabokov's exile. (Or does it have to do with his love of beaches?)
By the time the final major edition is released, it's earned a subtitle: "Speak, Memory: An Autobiography Revisited." By 1967, the author had written the book once, then translated it, then translated it back from Russian, having added new info from documents and sources that became available to him when World War Two was over and Europe, open again. The life of this book is for sure post-modern, a living text that shifted with the life of its author. The title totally reflects that.