--先删除下有vip=1的名称的vip=0的记录
DELETE FROM t WHERE isvip=0 AND EXISTS(SELECT * FROM t AS t0 WHERE t0.NAME=t.NAME AND t0.isvip=1)
--然后再执行你的 
--原来我是这样删除重复的：
delete from t where id not in (select min(id) from t group by name)

------解决方案--------------------

SQL code

IF EXISTS (SELECT 1 FROM SYSOBJECTS WHERE name = 'tba')
BEGIN
    DROP TABLE tba
END
GO
CREATE TABLE tba
(
    id INT,
    name VARCHAR(100),
    isVip INT
)
GO
INSERT INTO tba
SELECT 1,    'jc',    0 UNION ALL
SELECT 2,    'jc',    0 UNION ALL
SELECT 3,    'jc',    1 UNION ALL
SELECT 4,    'jc',    0 UNION ALL
SELECT 5,    'zz',    0 UNION ALL
SELECT 6,    'aa',    1 UNION ALL
SELECT 7,    'aa',    0 UNION ALL
SELECT 8,    'cc',    1
GO

delete from tba where id not in (select min(id) from tba AS A WHERE isVip = 1 OR NOT EXISTS (SELECT 1 FROM tba WHERE isVip = 1 AND A.name = name) group by name)

SELECT * FROM tba

------解决方案--------------------
SQL code
delete from tba
where exists (select 1 from (select row_number() over(partition by [name] order by [isVip] desc) rn, * FROM tba) t where t.rn<>1 and tba.id=t.id)

------解决方案--------------------

SQL code
--> 测试数据：[tb]
IF OBJECT_ID('[tb]') IS NOT NULL DROP TABLE [tb]
GO 
CREATE TABLE [tb]([id] INT,[name] VARCHAR(2),[isVip] INT)
INSERT [tb]
SELECT 1,'jc',0 UNION ALL
SELECT 2,'jc',0 UNION ALL
SELECT 3,'jc',1 UNION ALL
SELECT 4,'jc',0 UNION ALL
SELECT 5,'zz',0 UNION ALL
SELECT 6,'aa',1 UNION ALL
SELECT 7,'aa',0 UNION ALL
SELECT 8,'cc',1

--------------开始查询--------------------------

DELETE  a FROM [tb] AS a
WHERE id !=(SELECT TOP 1 id  FROM [tb] AS b WHERE b.[name]=a.[name] ORDER BY isVip DESC,[name]
)

----------------结果----------------------------
/* 
id          name isVip
----------- ---- -----------
3           jc   1
5           zz   0
6           aa   1
8           cc   1

(4 行受影响)
*/