@fhtino Thanks for your patience on this! I have checked with our App Service engineering team, they have confirmed that it's a bug, and the fix will be released in the next update (over few months | we don't have an exact ETA to share).
As and when I have more information, I'll share the update here.
At this moment, we don't have any workaround to add those custom hostname's in AppserviceHTTPLogs
for Linux apps.
Once again, thanks for reporting this issue. We appreciate your patience!
Feel free to reach back to me if you have any further questions on this.