Use python3 -m pip or python -m pip. That will use the correct pip for the python version you want. This method is mentioned in the pip documentation.
Symlinking python->python3 is a bad idea because some programs might rely on python being python 2. Though, I have seen some Dockerfiles symlink python->python3, like TensorFlow's CPU dockerfile (it's less of an issue in a Docker image). Coincidentally, that same Dockerfile uses the python3 -m pip install syntax that I recommend.
