I don't get it. You have a string as "Last Name, First Name" and you want Last Name, First Name without the quotes? Then just strip off the quotes. There is no need to use the split function. Since you want to break the name apart, my solution is actually correct. Remove the quotes, then split based on the comma.
I don't recall seeing that in the original post. I went back and re-read it, and if that is what the OP had intended, its a very poorly worded question . In this case, I'd:
string parts = Split(',')
foreach (string in parts)
Personally, parts 1 and 2 need special comma handling and parts 0 and 3 don't.
If I wanted to get sophisticated, I believe you can use datasets to parse something like that for you, but I'd just do what I said above... split on the commas, strip off the quotes and then process the 4 fields.