[Python] 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 3.8.0
pyenv 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.

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