直接修改报ORA-01109: database not open：

[oracle@prodb2 admin]$ . oraenv
ORACLE_SID = [prodb2] ? +ASM2
[oracle@prodb2 admin]$ sqlplus / as sysdba

SQL*Plus: Release 10.2.0.5.0 - Production on чǚϥ 7Ղ 6 02:24:48 2018

Copyright (c) 1982, 2010, Oracle.  All Rights Reserved.

Connected to:
Oracle Database 10g Enterprise Edition Release 10.2.0.5.0 - 64bit Production
With the Partitioning, Real Application Clusters, OLAP, Data Mining
and Real Application Testing options

SQL> 
SQL> 
SQL> alter user sys identified by admin;
alter user sys identified by admin
                             *
ERROR at line 1:
ORA-01109: database not open

10g中修改密码需要修改密码文件：

cd $GRID_HOME/dbs

WINDOWS:

orapwd file=/database/PWD.ora password=

UNIX:

orapwd file=/dbs/orapw password=

测试：

节点2修改密码：
[oracle@prodb2 ~]$ cd $ORACLE_HOME/dbs
[oracle@prodb2 dbs]$ orapwd file=orapw+ASM2 password=oracle force=y
[oracle@prodb2 dbs]$ sqlplus sys/oracle@asm2 as sysdba

SQL*Plus: Release 10.2.0.5.0 - Production on чǚϥ 7Ղ 6 02:43:25 2018

Copyright (c) 1982, 2010, Oracle.  All Rights Reserved.

Connected to:
Oracle Database 10g Enterprise Edition Release 10.2.0.5.0 - 64bit Production
With the Partitioning, Real Application Clusters, OLAP, Data Mining
and Real Application Testing options

SQL> 

节点1测试：
[oracle@ocm1 admin]$ sqlplus sys/oracle@asm2 as sysdba

SQL*Plus: Release 10.2.0.5.0 - Production on чǚϥ 7Ղ 6 02:45:31 2018

Copyright (c) 1982, 2010, Oracle.  All Rights Reserved.

Connected to:
Oracle Database 10g Enterprise Edition Release 10.2.0.5.0 - 64bit Production
With the Partitioning, Real Application Clusters, OLAP, Data Mining
and Real Application Testing options

SQL> show parameter remote_login_passwordfile

NAME                     TYPE           VALUE
------------------------------------ ---------------------- ------------------------------
remote_login_passwordfile        string         EXCLUSIVE

官方建议在修改密码前关闭asm实例，测试中未关闭，远程连接正常。

11g中修改密码相对简单：
single instance：

$ export ORACLE_SID=+ASM

$ asmcmd

ASMCMD> passwd sys
Enter old password (optional): 
Enter new password: ******

Cluster environment

ASMCMD> orapwusr --modify --password sys

Enter password: 
ASMCMD> exit

参考自：
How To Change ASM SYS PASSWORD ? (文档 ID 452076.1)
How to connect to ASM instance from a remote client (Oracle Net) (文档 ID 340277.1)