I also frequently start to think about the title, when the composition is finished. When I was young (up to 25) I had a mixture of "absolute music" titles and romantic programmatic titles (check my sparkles for two flutes, cello and harp for example). Recently several of my titles refer to social situation in the world. One of the pieces is called "At least five times useful", added with guarateed paper that the value won't expire after all five prelude-like movements are performed - as a mockery to recent creation of electronic devices, which frequently fail to work after their 2-year guarancee expires. I have also composed "Three days" for flute, saxophone and piano, recapturing the restless nature of our living, created in three-movement sonatina form. One of the compositions has the title "Illussion trio", refering to the cruel reality of modern, souless life.
Still, I most often write absolute music: Symphonies, concertos, different chamber works with titles refering to instrumental cast.