Depends on how you've written the beginning scene of each chapter. The benefit of including the character in the chapter title, is that it immediately grounds the reader in that particular point of view. This means less of those lurching few sentences of 'who the hell am I reading about here'. It also means there is no pressure to sneak in a solid tell of who the point of view is, which can be tricky without it seeming artificial.

So, if you've already written these scenes with the expectation that the character identity is obvious from the outset, you should definitely keep the character name chapter names. Personally, I prefer to opt for the immediate textual 'tell' of character identity, as it encourages you to strongly differentiate character voice, and it leaves more freedom for naming of chapter.

I wouldn't worry about it being too similar to GRRM in this sense. There are many authors who also include character name in the chapter title, James S.A. Corey, Adrian Tchaikovsky, etc. Neither would I worry about being similar in tone or setting. It's the similarity in plot or characters that will raise eyebrows in terms of plagiarism.