Here are two simple queries:
SELECT EntityID, EntityName FROM EntityRelations.Entities
WHERE EntityID IN (SELECT ModifiedByEntityID FROM EntityRelations.AssistanceFlags af WITH (nolock)
JOIN EntityRelations.Entities et WITH (nolock) ON af.EntityId = et.EntityId
WHERE ModifiedDate BETWEEN '6/1/12 3:00 AM'
AND '8/1/12 2:59 AM')
SELECT EntityName, Note, ModifiedByEntityID, ModifiedDate FROM EntityRelations.AssistanceFlags af WITH (nolock)
JOIN EntityRelations.Entities et WITH (nolock) ON af.EntityId = et.EntityId
WHERE ModifiedDate BETWEEN '6/1/12 3:00 AM'
AND '8/1/12 2:59 AM'
ORDER BY ModifiedDate ASC

The first gives a small table of names that I’d LIKE to slip into the second query into the ModifiedByEntityID field, having the names appear instead of the number.
EDIT by JerryB: I was getting an ambiguous EntityName message, so I adapted it to this, and it’s working perfectly, thanks: