Options for changing your account password differ with protocol you are using with your server. Most servers actually do not allow changing password using file transfer protocols used by WinSCP. In such case, you will need to use some alternative method.
SSH protocol allows changing an account password. But many SSH servers, notably the OpenSSH, does not actually allow that.
If your SSH server allows changing your account password, go to Session > Change Password to request that.
Also an SSH server can enforce password change on its own, e.g. in case the previous one expires. This can happen during authentication to the server. There are two possible methods, both are supported by WinSCP:
FTP protocol does not provide a method for changing an account password either.
Though various FTP servers support proprietary commands that can be used to change the password.
Some servers, such as Titan FTP server, support
SITE PSWD command:
SITE PSWD "<old_password>" "<new_password>"
Other servers, such as WS_FTP Server, support
Yet another variant is:
SITE CPWD <new_password>
You can execute any of these commands from Console window.
If you have a terminal (SSH) access to your server, change your password in the terminal session.
If you do not have a terminal access, your server administrator (e.g. webhosting providers) will have another method for changing a password (typically via their web site).