How are the jobs structured? If you are looking for a specific db, is this because you don't care about some, or you really need to know whether to respond? I'd think an alert would let a DBA log in and check which one is impacted.
If I needed to know which db is being backed up, I can look in sys.exec_requests for a backup command, but I think I'd be parsing looking for the backup log xxx and capturing the xxx. This gives you active backups:\
session_id as SPID, command, a.text AS Query, start_time, percent_complete,
dateadd(second,estimated_completion_time/1000, getdate()) as estimated_completion_time
FROM sys.dm_exec_requests r
CROSS APPLY sys.dm_exec_sql_text(r.sql_handle) a
WHERE r.command in ('BACKUP DATABASE')