Unfortunately there's no default way to do this in C#; At first when I looked at your question, I guessed that it may be something that setting the culture could fix, like:
string s = "SΨZΣ".ToLower(new CultureInfo("el-GR"));
but unfortunately this doesn't work. The problem is more complex, and therefore requires us to make our own solution:
public string GreekToLower(string s)
{
string lowerString = s.ToLower();
// Matches any 'σ' followed by whitespace or end of string
string returnString = Regex.Replace(lowerString, "σ(\\s+|$)", "ς$1");
return returnString;
}
This lowercases your string, and then looks for any 'σ' character that is followed by one or more whitespace or occurs at the end of the string (the last word in your string likely won't be followed by whitespace) and then replaces it with 'ς', preserving any existing whitespace it finds.
Regex is probably best suited for these types of scenarios. I'm guessing that you'll probably also want to make sure that the greek diacritics are added or removed as well, like the tonos for words like Ρύθμιση --> ΡΥΘΜΙΣΗ. This can be done, but it's way more complex and will require a more heavy regular expression to evaluate all cases.