pyenv does not change python version on mac

I installed pyenv on mac and have used the following commands to install the required python version:

pyenv install 3.8.0pyenv global 3.8.0

I am using zsh and my zshrc file contains the following:

if command -v pyenv 1>/dev/null 2>&1; then  eval "$(pyenv init -)"fi

When I check the python version, I can still see the old system version i.e. 2.7.15 responded by the command:

python -V

Any thoughts on what I might be doing wrong?

I have tried bash as well. I did not see any pyenv references in my bashrc file.