Part of the problem is that you over write your original query. Your OR operation would be equivalent to:
subquery1 = query.Where(obj=>obj.Id == id);
subquery2 = query.Where(obj=>obj.Name == name);
query = subquery1.Concat(subquery2).Distinct();
As you can see, that becomes pretty unwieldy as well, however if You are going to do this form, then you must maintain the original sequence so that you can get both the right and left sides of the equation processed then you need to be sure duplicates get removed.
Instead of all that, I would try to figure a way to build up that conditional statement dynamically using lambdas e.g.
I haven't actually run this, but something like this should work.
var cond = obj=>obj.Id == id;
...
// need an or
cond = obj=>cond(obj) || obj.Name == name;
query = query.Where(obj=>cond(obj));
Hope this gives you an idea.