Thats very good question actually! I checked my lab mgmt server and if you navigate to $FWDIR/log dir and then do command ls -lh *.log, you get bunch of files, BUT, none of them have gw name, just date and then .log at the end, as per below.
Andy
-rw-rw---- 1 admin root 20M Aug 29 00:00 2023-08-29_000000.log
-rw-rw---- 1 admin root 33M Aug 30 00:00 2023-08-30_000000.log
-rw-rw---- 1 admin root 25M Aug 31 00:00 2023-08-31_000000.log
-rw-rw---- 1 admin root 36M Sep 1 00:00 2023-09-01_000000.log
-rw-rw---- 1 admin root 28M Sep 2 00:00 2023-09-02_000000.log
-rw-rw---- 1 admin root 19M Sep 3 00:00 2023-09-03_000000.log
-rw-rw---- 1 admin root 19M Sep 4 00:00 2023-09-04_000000.log
-rw-rw---- 1 admin root 21M Sep 5 00:00 2023-09-05_000000.log
-rw-rw---- 1 admin root 23M Sep 6 00:00 2023-09-06_000000.log
-rw-rw---- 1 admin root 33M Sep 7 00:00 2023-09-07_000000.log
-rw-rw---- 1 admin root 26M Sep 8 00:00 2023-09-08_000000.log
-rw-rw---- 1 admin root 7.7M Sep 8 09:26 fw.log