It seems that what you mean by the phrase "extend my stay" is different from what most people interpret it as, so let's be specific.
When you enter the US on the Visa Waiver Program, you will be admitted for 90 days, unless your passport expires sooner than 90 days (in which case you will only be admitted until your passport expiration date). Even if your purpose is to only visit for a week, you will still be admitted for 90 days, because that is the standard procedure. (I am not sure whether it's possible for the officer to admit for a lesser time based only on discretion; there was some information that seemed to suggest they can't.) The date that you are admitted for will be on your I-94 (usually electronic I-94), and also usually written below your entry stamp.
When people say "extend my stay", they usually mean extend the amount of time one was admitted for (which for VWP is 90 days). Someone who is in the US on the Visa Waiver Program cannot apply for Extension of Status, though in extraordinary situations (e.g. natural disasters) it is possible to apply for something called "Satisfactory Departure", which will allow you to stay a given time longer without counting as having overstayed VWP.
If what you mean is that you changed your travel plans so that you are staying a different amount of time than what you told the officer, but it is all within the amount of time you were admitted for (e.g. for VWP, 90 days), then you are free to do that without notifying anyone or applying for anything.