Don't know what you mean by "file name of the project".
But, if Tomcat is deploying the war file using default config, the context path will be the name of the war file. So, if the war file is named
xyz.war, and the
servlet path is
/path-to-my-servlet, the URL would be
http://www.whatever.com/xyz/path-to-my-servlet.
This assumes deployment on port 80, and no Apache up-front doing URL shenanigans.