How do I create a dynamic environment variable?

You can inspect the branch name with TRAVIS_BRANCH.

Then, you can use bash indirection to get the value of the environment variable whose name is indicated by the value of TRAVIS_BRANCH:

$ PROD=1.0.1
$ STAGE=2.0.1
$ TRAVIS_BRANCH="PROD"
$ abc=${!TRAVIS_BRANCH}
$ echo ${abc}
1.0.1