SELECT
TableSource = CASE WHEN T1.[Name] IS NULL THEN 'Table2' ELSE 'Table1' END,
T1.[Name],
T1.[Address],
T2.[Name],
T2.[Address]
FROM [dbo].[My Table 1] T1
FULL OUTER JOIN [dbo].[My Table 2] T2
ON T1.[Name] = T2.[Name]
WHERE NOT T1.[Name] = T2.[Name]
For fast, accurate and documented assistance in answering your questions, please read this article.
Understanding and using APPLY, (I) and (II) Paul White
Hidden RBAR: Triangular Joins / The "Numbers" or "Tally" Table: What it is and how it replaces a loop Jeff Moden