Provided the date rows are always valid dates and follow a row with a name, there is this solution:

create table #test (Id int, Value varchar(25))

insert into #test

select 1, 'John Smith'

union select 2, '9/13/1961'

union select 3, 'Phony Persson'

union select 4, '2/24/1943'

union select 5, 'Doc Galacawicz'

union select 6, '11/11/1999'

SELECT a.Value, b.Value

FROM #test a INNER JOIN #test b on a.Id = b.Id - 1

AND ISDATE(b.Value) = 1

WHERE ISDATE(a.Value) = 0

ORDER BY a.Id