The name of Shropshire is derived from the Old English Scrobbesbyrigscīr, literally Shrewsburyshire. The former name for Shropshire, Salop, is derived from Salopesberia, an Anglo-French name.
"your name is" is correct English and when used in this way means both your full name or a part of your name (usually surname, depending on the context). "your names are" is also correct English, but...