var rtf = File.ReadAllText(fileName);
rtf = this.RenameStyleDifferentInOnlySpaces(rtf);
var document = provider.Import(rtf);

...

private string RenameStyleDifferentInOnlySpaces(string rtf)
{
    HashSet<string> styles = new HashSet<string>();

    string pattern = @"{\\(?:\*\\c)?s([0-9]+)[^}]*\n?[^}]*\\[^' ]* ?'?([^;]*)";

    var matches = Regex.Matches(rtf, pattern);
    foreach (Match match in matches)
    {
        string styleName = match.Groups[2].Value.Replace(" ", string.Empty);
        if (styles.Contains(styleName))
        {
            styleName = this.ReplaceOldStyleName(ref rtf, styles, match).Replace(" ", string.Empty);
        }

        styles.Add(styleName);
    }

    return rtf;
}

private string ReplaceOldStyleName(ref string rtf, HashSet<string> styles, Match match)
{
    string oldStyleName = match.Groups[2].Value;
    StringBuilder styleNameBuilder = new StringBuilder(oldStyleName + "0");
    while (styles.Contains(styleNameBuilder.ToString().Replace(" ", string.Empty)))
    {
        styleNameBuilder.Append("0");
    }

    string oldMatch = match.Groups[0].Value;
    string newMatch = oldMatch.Replace(oldStyleName, styleNameBuilder.ToString());
    rtf = rtf.Replace(oldMatch, newMatch);
    return styleNameBuilder.ToString();
}