Regex patterns C#

Rather than using a regex to check this I think I would write an extension method using Char.IsLetter(). You can handle multiple dashes then, and use languages other than English.

public static bool IsValidDashedString(this String text)
{
    bool temp = true;

    //retrieve the location of all the dashes
    var indexes =  Enumerable.Range(0, text.Length)
            .Where(i => text[i] == '-')
            .ToList();

    //check if any dashes occur, if they are the 1st character or the last character
    if (indexes.Count() == 0 ||
        indexes.Any(i => i == 0) ||
        indexes.Any(i => i == text.Length-1))
    {
        temp = false;
    }
    else //check if each dash is preceeded and followed by a letter
    {
        foreach (int i in indexes)
        {
            if (!Char.IsLetter(text[i - 1]) || !Char.IsLetter(text[i + 1]))
            {
                temp = false;
                break;
            }
        }
    }

    return temp;
}

The following will match a string with one alphabetic character before the "-" and one after:

[A-z]-[A-z]

You may need to first test whether there is "-" present if that is not always the case. Could do with more information about the possible string contents and exactly why you need to perform the test

(^.+)(\D+)(-)(\D+)(.+)

I have tested this for some examples here http://regexr.com/39vfq