Надо менять скрипт бэкапа
Например вот так
Код:

DECLARE @dateString CHAR(12), @daySTR CHAR(2), @monthSTR CHAR(2), @hourSTR CHAR(2), @minSTR CHAR(2)
--month variable
IF (SELECT LEN(CAST(MONTH(GETDATE()) AS CHAR(2))))=2
SET @monthSTR=CAST(MONTH(GETDATE()) AS CHAR(2))
ELSE
SET @monthSTR= '0' + CAST(MONTH(GETDATE()) AS CHAR(2))
--day variable
IF (SELECT LEN(CAST(DAY(GETDATE()) AS CHAR(2))))=2
SET @daySTR=CAST(DAY(GETDATE()) AS CHAR(2))
ELSE
SET @daySTR='0' + CAST(DAY(GETDATE()) AS CHAR(2))
--hour variable
IF (SELECT LEN(DATEPART(hh, GETDATE())))=2
SET @hourSTR=CAST(DATEPART(hh, GETDATE()) AS CHAR(2))
ELSE
SET @hourSTR= '0' + CAST(DATEPART(hh, GETDATE()) AS CHAR(2))
--minute variable
IF (SELECT LEN(DATEPART(mi, GETDATE())))=2
SET @minSTR=CAST(DATEPART(mi, GETDATE()) AS CHAR(2))
ELSE
SET @minSTR= '0' + CAST(DATEPART(mi, GETDATE()) AS CHAR(2))
--name variable based on time stamp
SET @dateString=CAST(YEAR(GETDATE()) AS CHAR(4)) + @monthSTR + @daySTR + @hourSTR + @minSTR
--=================================================================
DECLARE @SQL VARCHAR(1000), @DBNAME VARCHAR(200), @CheckResult VARCHAR(200), @PDASERVER as varchar(20)
SELECT @DBNAME = NAME FROM sys.databases WHERE name like '%Название базы%'
SELECT @SQL = 'BACKUP DATABASE '+@DBNAME+' TO DISK = ''E:\Backup\'+@DBNAME+'_db_' + @dateString +'.bak'' WITH INIT'
EXEC (@SQL)
Ессно вместо названия базы пишете свою базу и путь напишите свой, а с датой думаю поиграете как надо будет
