If you get this error and all else is as it should be, try this.
Msg 14607, Level 16, State 1, Procedure sysmail_verify_profile_sp, Line 42
profile name is not valid
Run this and then the TestSQL output to make sure you've really got the correct Profile name.
SELECT [profile_id]
,[name]
,[description]
,[last_mod_datetime]
,[last_mod_user]
,'EXEC msdb.dbo.sp_send_dbmail
@profile_name = ''' + name + ''',
@recipients = ''me@test.com'',
@subject = ''Test'',
@body = ''Message'',
@body_format = ''HTML'';' AS TestSQL
FROM [msdb].[dbo].[sysmail_profile]