feat(otel): set default_log_name for GCP logging exporter

Uses value of GCP_DEFAULT_LOG_NAME env var if it exists, defaults to literal adk-otel.

PiperOrigin-RevId: 817125337

src/google/adk/telemetry/google_cloud.py

@@ -15,6 +15,7 @@
 from __future__ import annotations
 
 import logging
+import os
 from typing import cast
 from typing import Optional
 from typing import TYPE_CHECKING
@@ -37,6 +38,9 @@ if TYPE_CHECKING:
 
 logger = logging.getLogger('google_adk.' + __name__)
 
+_GCP_LOG_NAME_ENV_VARIABLE_NAME = 'GOOGLE_CLOUD_DEFAULT_LOG_NAME'
+_DEFAULT_LOG_NAME = 'adk-otel'
+
 
 @experimental
 def get_gcp_exporters(
@@ -118,9 +122,13 @@ def _get_gcp_metrics_exporter(project_id: str) -> MetricReader:
 def _get_gcp_logs_exporter(project_id: str) -> LogRecordProcessor:
   from opentelemetry.exporter.cloud_logging import CloudLoggingExporter
 
+  default_log_name = os.environ.get(
+      _GCP_LOG_NAME_ENV_VARIABLE_NAME, _DEFAULT_LOG_NAME
+  )
   return BatchLogRecordProcessor(
-      # TODO(jawoszek) - add default_log_name once design is approved.
-      CloudLoggingExporter(project_id=project_id)
+      CloudLoggingExporter(
+          project_id=project_id, default_log_name=default_log_name
+      ),
   )