You can use the Enumerable.Where extension method:
var matches = myList.Where(p => p.Name == nameToExtract);
Returns an IEnumerable<SampleClass>. Assuming you want a filtered List, simply call .ToList() on the above.
By the way, if I were writing the code above today, I'd do the equality check differently, given the complexities of Unicode string handling:
var matches = myList.Where(p => String.Equals(p.Name, nameToExtract, StringComparison.CurrentCulture));