How long before Google will update search terms matching my website?
 

[B]I have a site which title I changed about a month ago. The site is a classifieds website which is powerful, using php.

I had a very similar case, also with a lassifieds site. Google updated it only after all classifieds from my site that were posted before I changed its name had expired.

I think you need to do more work for your website and generate more backlinks.