As with any industry, or branch of the arts, there are always the talented-but-not-household names. My first answer to this question would be a gentlemen by the name of Craig Carothers (craigcarothers.com). I’m lucky enough to call him a friend and mentor.
His major break came when his song “Little Hercules” was placed on Trisha Yearwood’s album “Everybody Knows” in 1996. Since then he has had numerous placements on albums, and in film and TV alike, but he has yet to match the success of that song. In my opinion he has numerous songs that are as good and should be country hits, so I would urge you to check him out. His track “Just to Say I Did” remains one of my all-time favorite songs, and brings me to tears whenever I listen to it.
An easy way to find more answers to this question is to search for some of your favorite songs on Wikipedia, and look at the list of people in the “songwriter” section. Oftentimes there will be multiple writers on a song, and many of them you might not have heard of. Look up their individual websites and you will see what they are working on on their own. Artists (like Lady Gaga) will often start as a co-writer for other artists, flying under the radar, before breaking out on their own.
For me, a recent example would be Fiona Bevan, co-writer on the Backstreet Boys’ recent hit song “Chances”. I had never heard of her, but am now aware of her and will be keeping an eye on what she releases next.
Short answer… there are a LOT of them. 🙂