List.Any get matched String

Not with Any, no... that's only meant to determine whether there are any matches, which is why it returns bool. However, you can use FirstOrDefault with a predicate instead:

var match = FilePrefixList.FirstOrDefault(s => FileName.StartsWith(s));
if (match != null)
{
    // Display the match
}
else
{
    // Nothing matched
}

If you want to find all the matches, use Where instead.