Solution 1:

You should be using DATEADD is Sql server so if try this simple select you will see the affect

Select DATEADD(Month, -1, getdate())

Result

2013-04-20 14:08:07.177

in your case try this query

SELECT name
FROM (
SELECT name FROM 
Hist_answer
WHERE id_city='34324' AND datetime >= DATEADD(month,-1,GETDATE())
UNION ALL
SELECT name FROM 
Hist_internet
WHERE id_city='34324' AND datetime >= DATEADD(month,-1,GETDATE())
) x
GROUP BY name ORDER BY name

Solution 2:

Try this : Using this you can select date by last 30 days,

SELECT DATEADD(DAY,-30,GETDATE())