Include logger name in FnApiLogRecordHandler log entries

[hjtran]

The FnApiLogRecordHandler creates LogEntry protos but doesn't include the logger name (record.name). This is useful for filtering and debugging logs in complex pipelines.

Proposal: Add the logger name to custom_data:

log_entry.custom_data['logger'] = record.name

[userzhy]

I have submitted a PR #37177 to address this. PTAL when you have time! Thanks.