What is the meaning of gaga and Lady Gaga?

Everyone knows Lady Gaga but does anyone know what is the meaning of Gaga? According to web definition, gaga (pronounce /’gä,gä/), means overexcited or irrational, typically as a result of infatuation or excessive enthusiasm; mentally confused; senile. According to dictionary, gaga means crazy; silly; dotty; demented; ardently fond; infatuated; excessively and foolishly enthusiastic. In a nutshell, Lady Gaga means a lady that is overexcited, irrational, excessive enthusiasm in music, mentally confused in dancing, and a foolishly enthusiastic for music. Correct?  Whatever it means, everyone in the world now is gaga over Lady Gaga’s music.