C# - Get A List Of Distinct Items And Their Count?

I have an object, that has many properties but the only two to worry about are:

myobject.ID which is an int
myobject.Names which is a HashSet

Then I have a List of those objects that looks something similar to this:

List<myobject>

I use Linq to get a some of the data into a repeater, but I'm not sure how to get the list of Names and how often they show up.

Want to use Linq to avoid having to loop through the data.

As my tags should show, this is an ASP.NET solution using C#.

Some clarification:
Lets say I have just three items in my list:
Item 1 has John, Fred, Jack in its names.
Item 2 has John, Fred, Joe in its names.
Item 3 has John in its names.

I am trying to return the following:
John - 3
Fred - 2
Jack - 1
Joe - 1

Also, as a note I am familiar with having to write my own comparer for my object, I'm just missing the 'how to' for the overall solution in my thoughts.