How to merge two lists using LINQ?

I would strongly recommend against using string-concatenation to represent this information; you will need to perform unnecessary string-manipulation if you want to get the original data back later from the merged list. Additionally, the merged version (as it stands) will become lossy if you ever decide to add additional properties to the class.

Preferably, get rid of the Merge method and use an appropriate data-structure such as a multimap that can each map a collection of keys to one or more values. The Lookup<TKey, TElement> class can serve this purpose:

var personsById = list1.Concat(list2)
                       .ToLookup(person => person.ID);

Anyway, to answer the question as asked, you can concatenate the two sequences, then group persons by their ID and then aggregate each group into a single person with the provided Merge method:

var mergedList = list1.Concat(list2)
                      .GroupBy(person => person.ID)
                      .Select(group => group.Aggregate(
                                         (merged, next) => merged.Merge(next)))
                      .ToList();

EDIT: Upon re-reading, just realized that a concatenation is required since there are two lists.