Yes, there is a name for the tear...it's called an anal fissure. I have had them for almost 2 years now. At the time, the colorectal doctor gave me some creams and told me to take Metamucil and drink water.
Then he recommended surgery...I was reluctant, and so I never did it.
I still suffer with pain (almost daily) and bleeding (only occassionally). I still take Metamucil, exercise, drink lots of fluids (mostly water) and do yoga for stress management. However, I have good days and bad days. I think that despite my best efforts, my stressful job gets the best of me.
(For example, over the holidays when I was away from work for a few days, my BM's were great! Almost no pain! Two days back at work and I'm bleeding again....it's like torture.)
Aside from surgery, I don't think I have other options. I am not going to become dependent on laxatives or stool softeners..frankly my stool is fairly soft most of the time, I think that the tears were so bad that I still get injured even with the passage of a normal BM.
I don't think there are long term effects (ie, you can't get cancer from it or anything)...for me the only effects are on my psyche.
I just try to do my best to stay healthy...
Best of luck to you...let me know how you're doing!
Hope this helps...