Yes, at least to an extent. You can of course change the name of 'Terminal.app' to 'myTerminal.app' and this would change the label of the shortcut on the dock.
Alternatively you could modify the 'file-label' tag inside of ~/Library/Preferences/com.apple.dock.plist though I suspect this to be a temporary change since the plist values will overwrite once the app is launched.
Your second request is much more simple to accomplish, simply enter any command you want executed when opening Terminal.app into a text file called .bash_profile inside your home directory, this file is executed every time Terminal is opened.
I'd like to also suggest an alternative solution, it sounds like your trying to create a shell script that can be launched from the dock, create a text file with any shell scripts you wanted to execute, then remove .txt and replace with .command and you have a shell script that can execute from the Finder.