To start, let me mention that I am a Russian citizen. On the other hand, I am not involved in politics anyhow, so what I am saying here is some kind of a thoughts of a random guy from Russian streets. Well, of a random guy who visits stackoverflow.
Short answer is: No, nothing changed.
But I need to mention that the renaming was a part of a bigger process. The idea was to build the law- enforcement system from ground up. This was achieved by dismissing every member of militia and making them to pass a special exam. If the member of militia passes the exams he or she gets hired into newly created institution - Police. These would have helped to make a 'clean start' for new institution, keeping only 'good cops' and dismissing those which are not professional enough/corrupted. New name and new uniform would have helped to make some distance between new police and crimes committed by old militia and would help to improve image of law enforcement.
Unfortunately, this campaign have failed miserably. There were tons of reports that people who were responsible for transfer from militia to police were corrupted and transferred to police almost anyone who willed to pay. At the same time 'good cops' who weren't corrupted often were dismissed completely and weren't transferred to police. So as result this renaming operation actually achieved the opposite - it kept almost all of the bad guys but some of the good policemen were lost during transfer. The cases were reported more or less widely.
At the same time shortly after renaming finished new reports of police crimes appeared which further hurt image of the newly created police.
Finally I need to mention that we had a rather serious public unrest between 2011 and 2013 where police actively participated in dispersal of peaceful demonstrations which further hurt the image of the police.
On the other hand I need to mention that the world seem a rather dangerous place for people here, and that pushes up the approval ratings for police since people look for protection from law enforcement.
That combined leads to the fact that most likely the image of police is better than one of the old militia (prior to renaming) but the difference is negligible.
Finally I need to touch the surveys-related part of your question. Unfortunately, I can't provide you with a links to such surveys in English. But I can reassure you that there was no such big and comprehensive survey performed by any agency not strongly tied to the government. All small non-government surveys are not representative (since they were performed by small web-sites and a biased one way or another) and usually show no difference in perception of police and militia.