Does adding professors' names in the acknowledgement section influence acceptance of a paper?

For reputable journals, including the names of prominent researchers should not influence the acceptance of a paper, and in the top tier journals I expect this would certainly be the case.

It would be easy (but not ethical) to include the names of prominent or famous researchers in acknowledgements or as co-authors in the hope of influencing a decision for acceptance but reputable journals will not publish something that does not meet their publication standard.

If prominent researchers have provided feedback or otherwise helped with the writing (but not to the extent that they would be co-authors) then it is appropriate to include them in the acknowledgements.

Also, some journals only forward the text (without authors or acknowledgements) to reviewers in the interests of having impartial reviews, so that the reviewers will not see names and then not be influenced to recommend acceptance for a paper they might otherwise reject.

For not-so-reputable journals, they will publish regardless of the names (and if a paper includes the names of prominent researchers, the journal will sit securely behind the declaration that the submitting author has signed).

I believe it does affect positively the acceptance of a paper. Pre-publication peer review is biased by a number of factors, particularly the typically low number of reviews, their brevity and superficiality, the secrecy around what happens, field politics.

In fact, I believe my name is being recurrently added to the acknowledgements section of a number of papers issuing from a bad group I recently happened to work with. These people believe I am fairly well-known in our field of research, and probably seek to avoid me as a reviewer. They have first-hand told me other manoeuvres locally (nationwide) employed to skew peer reviews and papers' acceptance. Also I am aware of a number of "reputable professors" who actually secretly pass on their review assignments to PhD students and postdocs who just want to "be done with that" -- likely these are reviewers who will cling onto just anything to support accepting/rejecting a paper.

So, if you wish to use this as an asset to speed up acceptance of your paper, go ahead. The system as it is remains quite open to manipulation. However do fear a few judicious reviewers and readers that do exist everywhere, particularly after publication of your paper. The weaknesses of your manuscript might be so easy to spot and expose that a single easily-published paper might be your reputation's demise. A late public exposure that could be avoided with the help of a couple of good reviewers.

Good luck, and welcome to the Academia.

P.S. Please note that I am not saying that you ought not to add names of contributors to your acks section. These people must be acknowledged for their participation. Also I am not saying that you necessarily seek to game the system: you're just asking here because you're curious. I am warning you and other passersby of some reality in relying on peer-review and paper acceptance gimmicks as 'scientific career shortcuts'.