applied fixes from comments

Author: Nayeem Kamal

dd-java-agent/agent-llmobs/src/main/java/datadog/trace/llmobs/LLMObsSystem.java

@@ -12,7 +12,7 @@
 import java.lang.instrument.Instrumentation;
 import java.util.Map;
 import java.util.concurrent.TimeUnit;
-import org.jetbrains.annotations.Nullable;
+import javax.annotation.Nullable;
 import org.slf4j.Logger;
 import org.slf4j.LoggerFactory;
 
@@ -191,15 +191,22 @@ public LLMObsSpan startWorkflowSpan(
 
     @Override
     public LLMObsSpan startEmbeddingSpan(
-        String spanName, @Nullable String mlApp, @Nullable String sessionId) {
-      return new DDLLMObsSpan(
-          Tags.LLMOBS_EMBEDDING_SPAN_KIND, spanName, getMLApp(mlApp), sessionId, serviceName);
+        String spanName,
+        @Nullable String mlApp,
+        @Nullable String mlProvider,
+        @Nullable String sessionId) {
+      if (mlProvider == null) {
+        mlProvider = "custom";
+      }
+      DDLLMObsSpan embeddingSpan =
+          new DDLLMObsSpan(
+              Tags.LLMOBS_EMBEDDING_SPAN_KIND, spanName, getMLApp(mlApp), sessionId, serviceName);
+      embeddingSpan.setTag("ml.provider", mlProvider);
+      return embeddingSpan;
     }
 
     public LLMObsSpan startRetrievalSpan(
-        String spanName,
-        @javax.annotation.Nullable String mlApp,
-        @javax.annotation.Nullable String sessionId) {
+        String spanName, @Nullable String mlApp, @Nullable String sessionId) {
       return new DDLLMObsSpan(
           Tags.LLMOBS_RETRIEVAL_SPAN_KIND, spanName, getMLApp(mlApp), sessionId, serviceName);
     }

dd-trace-api/src/main/java/datadog/trace/api/llmobs/LLMObs.java

@@ -47,8 +47,11 @@ public static LLMObsSpan startWorkflowSpan(
   }
 
   public LLMObsSpan startEmbeddingSpan(
-      String spanName, @Nullable String mlApp, @Nullable String sessionId) {
-    return SPAN_FACTORY.startEmbeddingSpan(spanName, mlApp, sessionId);
+      String spanName,
+      @Nullable String mlApp,
+      @Nullable String mlProvider,
+      @Nullable String sessionId) {
+    return SPAN_FACTORY.startEmbeddingSpan(spanName, mlApp, mlProvider, sessionId);
   }
 
   public LLMObsSpan startRetrievalSpan(
@@ -102,7 +105,10 @@ LLMObsSpan startWorkflowSpan(
         String spanName, @Nullable String mlApp, @Nullable String sessionId);
 
     LLMObsSpan startEmbeddingSpan(
-        String spanName, @Nullable String mlApp, @Nullable String sessionId);
+        String spanName,
+        @Nullable String mlApp,
+        @Nullable String mlProvider,
+        @Nullable String sessionId);
 
     LLMObsSpan startRetrievalSpan(
         String spanName, @Nullable String mlApp, @Nullable String sessionId);

dd-trace-api/src/main/java/datadog/trace/api/llmobs/noop/NoOpLLMObsSpanFactory.java

@@ -37,7 +37,10 @@ public LLMObsSpan startWorkflowSpan(
   }
 
   public LLMObsSpan startEmbeddingSpan(
-      String spanName, @Nullable String mlApp, @Nullable String sessionId) {
+      String spanName,
+      @Nullable String mlApp,
+      @Nullable String mlProvider,
+      @Nullable String sessionId) {
     return NoOpLLMObsSpan.INSTANCE;
   }