When I start composing a piece of music it usually is because there is a melodic phrase POUNDING between my ears. Most instances there is no name for that music so the piece gets started with a number as the file name.
When I switched to using Finale for scoring I started using Opus numbers so that I would have a convenient way of naming files. Up until Hurricane Katrina I had just over 300 pieces of handwritten music stored in my lockable file box. When the box was stolen I started numbering at 313 to be sure there was no overlap of the earlier pieces. There was a slim hope that the filebox would be recovered and I didn't want to renumber later. I actually think 307 was the last piece prior to Katrina, but the memory is questionable.
I have recovered the first and second pieces I wrote. They were both written at Blair Academy. "The Hermit" for Oboe and Strings has never been performed although the computer playback is great. "Two Flutes and a Cello" was performed at Blair by myself and classmates Louise Ewing and Donald Blocker. (I have mentioned this before.) At least a few of our classmates were actually at the Headmaster's home for that performance. Not an exciting name for the piece, but it certainly was descriptive. As a tidbit, the only other piece I have written which is named for the instruments it uses is "Trombone and Timpani, with Piano and Strings".
Three other pieces, "Sarah's Trumpet," "Horn March," and "Brash Brass" have different stories. Both Sarah's and Horn were written for Recorder although the Sarah in question was actually a trumpet player and both are now stored on my computer with brass voices instead of Recorder. Brash Brass is an eighteen-voice brass piece that was written for a Dallas Symphony contest but due to illness was not completed in time to meet the deadline.
Names for my music generally come to me as I am completing the work, or later when I am rehearsing it. Some of my music has remained numbered and hence, unnamed, for years until the feeling that I knew the name I wanted came over me.
On the other hand, I do have pieces that are named from their very first note. Some of these are the four piece Blue Ridge Mountains Water Music, Sorcha Lawhir, and Shasta Snow Light. At a guess I would say that maybe 30-35% of my music compositions start out with names.
On the other hand, some are actually renamed because the music evolved as it was being written from the concept the name originally portrayed. Some had names applied for competitions and then renamed when I didn't win, and others get renamed to fit or to honor individuals such as "Susan's Concerto" for Englilsh Horn, Bassoon and Violin or "Bodil Diesen" who is the maker of two of my Recorders. And a few still bear the "Ode" titles with a number because I couldn't remember the original purpose of the music.
So is there an art to naming music? Most assuredly, but it is exercised differently for each composer. As a larger portion of my works are for solo performance it would be repetitive to name the piece for the type and number of instruments. Just a number for a name doesn't feel right to me. But still, at times the name is nothing more than a convention because it gets attached to the music that has been struggling to get out of my head.
One thing I promised myself was to never name a piece for the key it was written in. As an example, consider a Dance in A-minor; once it get's transposed it is no longer a Dance in the original key. So at least I have one restriction in my naming process even if the others all more closely follow gut reaction.