Try this:
public static Regex regex = new Regex(
"(?<=<span class=\ \ \"nameLastname\ \ \">)(?<Name>.*)(?=</span>)",
RegexOptions.Singleline
| RegexOptions.CultureInvariant
| RegexOptions.Compiled
);
public static string regexReplace =
"Dave";
string result = regex.Replace(InputText,regexReplace);
[edit]Remove the spaces between the backslashes - otherwise Markdown swallows parts of the regex...[/edit]