In this video, I talk about the likelihood that your unwanted negative suggestions might go away naturally all by themselves.
We've seen this happen before, but it usually takes several months. One problem is that once a suggestion appears after your name or business name, people click on it out of curiousity - even if that was not their original intention.
So, unfortunately, once a suggestion gets there, it can be tough to get rid of by doing nothing. That being said, I have seen it happen - Google is constantly updating the autocomplete algorithm to make it more useful.
And in some cases, I've seen Google remove suggestions entirely. for example, you won't see pornographic or ethnic-related suggestions.
I've seen "racist" disappear naturally and it also looks like "arrest" is no longer showing, by default.
So, if you don't have the budget and want to wait, it is possible that your problem can clear up naturally over time.