Connecting by hostname requires that you go through hostname to IP resolution. That's handled by the hosts file and falls back to DNS. This all happens before you ever touch the docker container, and docker machine itself does not have any external hooks to go out and configure your hosts file or DNS servers.
With newer versions of Docker on windows, you run containers with HyperV and networking automatically maps ports to localhost so you can connect to http://localhost. This won't work with docker-machine since it's spinning up virtualbox VM's without the localhost mapping.
If you don't want to configure your hosts file, DNS, and can't use a newer version of docker, you're left with connecting by IP. What you can do is use a free wildcard DNS service like http://xip.io/ that maps any name you want, along with your IP address, back to that same IP address. This lets you use things like a hostname based reverse proxy to connect to multiple containers inside of docker behind the same port.
One last option is to run your docker host VM with a static IP. Docker-machine doesn't support this directly yet, so you can either rely on luck to keep the same IP from a given range, or use another tool like Vagrant to spin up the docker host VM with a static IP on the laptop. Once you have a static IP, you can modify the host file once, create a DNS entry for every dev, or use the same xip.io URL, to access the containers each time.