Here are two examples of how you could do that.
--method #1
with MyAddresses as
(
select a.name, b.address, ROW_NUMBER() over (partition by a.name order by (select null)) as RowNum
from a left outer join b on a.name = b.name
)
select *
from MyAddresses
where RowNum = 1
--Method #2
select *
from
(
select a.name, b.address, ROW_NUMBER() over (partition by a.name order by (select null)) as RowNum
from a left outer join b on a.name = b.name
)x
where x.RowNum = 1
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