I don’t recall if I set those items in the past, so perhaps they are the OS X default, but they are controlled in Terminal by opening the Preferences and clicking on Window. Here you can title the window bar with your own text, and then there are check boxes for various other things like the active process (your shell name if idle).

this is not always true and you should not rely on it. From the bash man page:

SHELL The full pathname to the shell is kept in this environment variable.
If it is not set when the shell starts, bash assigns to it the full
pathname of the current user’s login shell.

This means that if it is already set a new shell will not replace the value on startup.

tcsh and ksh behave the same way:

$ echo $SHELL
/bin/bash
$ tcsh
% echo $SHELL
/bin/bash
% ksh
> echo $SHELL
/bin/bash

Matteo