There are two places that copies of an account's password may exist. One is on the computer where you have the account; the other is on your Macintosh, in the account description. You can change either copy, or both at once.
The other computer will likely provide a command you can type to change its idea of your password. If so, this command can be given by picking the Password command from the Commands menu.
With the Password command, the new password will be stored on the other computer and in the account description on the Macintosh at the same time. (It won't be stored on the Mac unless the old password was also stored, though.)
If you just type the other computer's command and bypass the Commands menu, then the password stored in the account description will no longer be accurate.
To change only the copy stored in the account description, first open the description using the Accounts command in the Settings menu. The account description contains a check box marked "Password Saved in TT Memory". Uncheck it if it is already checked; then check it. When you check it, you will be asked for a new password. Give one, press OK, and the new password has been saved on the Macintosh.
(An incidental note: Rarely does the other computer actually store your password as such, since that would be insecure. Instead, a non-reversible cryptographic transformation is applied to your password before it is stored. When you connect and give the password later, the password you type is subjected to the same transformation and compared to the stored transformed copy.)
