Once you execute it’s no longer an idea, it’s a thing you did that the other person did not. It’s honorable to share your inspiration from the idea of another, but that person does not deserve credit for your work thus can claim no credit. So yes it’s not only okay, but it’s the only thing that makes sense.

Don't lie, but you also don't need to be as self-sacrificing as the department of ideas. If the seed of the idea came from someone else and then you iterated on it and made it into a serious thing, you should give them credit for the original idea, but you can take credit for all the things you added and the effort you put into making it happen.