The first part of the log name is the application GUID. I get the application GUID and search on the GUID.
If I need to find something in multiple applications, I create a table of the application GUIDs manully or by querying the repository database. I then load the table into a Python script to search the script folder
Can you explain a bit more what you're trying to accomplish and why? As you've found, by default, the app's name is not written to the log file. As @jwjackso pointed out, the app's ID is in the filename which can be used to join together information in a pinch.
To the background: Different load scripts are running on my server at different times. The data is delivered via FTP. Unfortunately errors often occur because the formats are not adhered to or columns are missing. I would then like to read out the log files and send notes to the data suppliers by email. Since Filemaker is also running on the server, the plan is to do this via Filemaker. It's a kind of alert function.