You can set image name when building a custom image, like this:

docker build -t dude/man:v2 . # Will be named dude/man:v2

Is there a way to define the name of the image in Dockerfile, so I don't have to mention it in the docker build command?

Workaround using docker-compose

Tagging of the image isn't supported inside the Dockerfile. This needs to be done in your build command. As a workaround, you can do the build with a docker-compose.yml that identifies the target image name and then run a docker-compose build. A sample docker-compose.yml would look like

version: '2'

services:
  man:
    build: .
    image: dude/man:v2

That said, there's a push against doing the build with compose since that doesn't work with swarm mode deploys. So you're back to running the command as you've given in your question:

docker build -t dude/man:v2 .

Personally, I tend to build with a small shell script in my folder (build.sh) which passes any args and includes the name of the image there to save typing. And for production, the build is handled by a ci/cd server that has the image name inside the pipeline script.