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).