Back up your database before running any conversions! Note that I doubt the suggested fix will help at all.
If you could give us a sample of "wrong" name and what it's supposed to be, we could be of more help. You said there was a major server change? Have you checked that the page has the correct encoding, and that the server is sending it with that encoding and not overriding it to another encoding? That is, if your page is supposed to be UTF-8 (and the <meta> tag says so), do a browser View > Character Set Encoding and see if that's what's actually being displayed. I have seen servers configured to override UTF-8 requests with Latin-1.
If the page display is OK, might the database server been changed? Is it still holding text data in the correct encoding? Remember that MySQL's default is Latin-1, so if the database was recreated as part of this configuration change, and you forgot to change it to UTF-8, that could be a problem.