USA tourist visa question

I arrived into the US on a tourist visa planning to stay for 1 month, but for reasons out of my control I need to extend my stay 1 extra month, that's still within the 3 months that the tourist visa allows, but my doubt is that the return date I gave at border police is obviously not true anymore.

Is it legal to stay longer than the date I gave at customs, as long as I stay within the 3 months awarded by a tourist visa? Do I have to call someone to update my information in both time and place of stay? I tried looking for answers online but couldn't find anything.