Failed to notify ''operator name'' via email?...

First Check the value for Database mail profile is NUll

EXEC master.dbo.xp_instance_regread N'HKEY_LOCAL_MACHINE', N'SOFTWARE\Microsoft\MSSQLServer\SQLServerAgent', N'DatabaseMailProfile'

If So

select 'exec master.dbo.xp_instance_regwrite N''HKEY_LOCAL_MACHINE'', N''SOFTWARE\Microsoft\MSSQLServer\SQLServerAgent'', N''DatabaseMailProfile'', N''REG_SZ'', N''' + name + ''''
from msdb.dbo.sysmail_profile
where profile_id in (Select profile_id from msdb.dbo.sysmail_principalprofile )

Copy the output and Execute, it will be as below

exec master.dbo.xp_instance_regwrite N'HKEY_LOCAL_MACHINE', N'SOFTWARE\Microsoft\MSSQLServer\SQLServerAgent', N'DatabaseMailProfile', N'REG_SZ', N'DBA'

Now Restart the SQL Agent. mail will work now.


------------------------------ OR --------------------------------

Verify below Steps are configured properly or not

1. Enable database mail, create a new profile and mail account

2. Right click SQL Agent>Properties>Alerts System>Enable Mail Profile

3. Expand SQL Agent>Operators>Create New Operator

Configuring above steps will work make DB mail to work properly.