Is there a way I can only enable the system to send password change email. Currently it appears, if I turn off verification email, it does not send password change email.
Those two templates should not be related in the manner you describe. I just tested this in my own tenant by disabling the verification email template through the dashboard and then proceeding to request a password reset to my user; this resulted in me receiving the reset password email as expected.
Have in mind that although the dashboard user interface does not show a toggle for the reset password email template the template itself can still be disabled individually so you should review if you’re not in the situation described in this other post: