There are several utilities that accomplish this. I will give you two.
Greenshot
It is free an open source. You can set it to automatically save the screenshot to a specific folder with a specific name. You can even have it automatically copy the file path for you.
Snagit
The other option that I would suggest is Snagit by Techsmith. It can accomplish the same thing as Greenshot and it has a lot more features as well. This one is not free or open source tho.