Is it possible to add a function within a function?

function update_profile
{
    echo "1. Update Name"
    echo "2. Update Age"
    echo "3. Update Gender"
    echo "Enter option: "
    read option

    case $option in
         1) update_name ;;
         2) update_age ;;
         3) update_gender ;;
    esac

    function update_name
    {
        echo "Enter new name: "
        read name
    }
}

My code, but incomplete, just want to make sure if it's possible to do this way. I do know that i can throw all the codes into the case, but it will be messy, so I was thinking to create a stand alone function, within a function, and to be called when needed to perform it's commands.