If there is already a relationship between them (because you, for example, set one of them in the designer), you should simply do:
var foo = db.ParentDataItems.Where(p => p.ChildDataItems.Any(c => c.Name == "value");
Which will receive any parent data items that have children with a name matching "value".
, ( ):
var foo = db.ParentDataItems.Join(db.ChildDataItems.Where(c => c.Name == "value"),
p => p.ChildDataItemId,
c => c.ParentDataItemId,
(parent, child) => parent);