If you want to change your Google Account password, you should once in a 3 month at least, to make sure nobody hacked your account, incuding your android phone
To change the password for your Google Account, just follow these steps:
Visit the Google Accounts security tab .
If you’re not already signed in to your Google Account, enter your username and password, and click Sign in .
Click Change your password .
If you’re unable to sign in to your Google Account, or you’ve forgotten your password, just enter your username on the password-assistance page to reset your password and regain access to your account. It will show a few ways to reset password