diff --git a/tests/entrypoints/openai/test_serving_engine.py b/tests/entrypoints/openai/test_serving_engine.py
index 6199a75b5b4f8..096ab6fa0ac09 100644
--- a/tests/entrypoints/openai/test_serving_engine.py
+++ b/tests/entrypoints/openai/test_serving_engine.py
@@ -9,6 +9,7 @@
                                               LoadLoraAdapterRequest,
                                               UnloadLoraAdapterRequest)
 from vllm.entrypoints.openai.serving_engine import BaseModelPath, OpenAIServing
+from vllm.lora.request import LoRARequest
 
 MODEL_NAME = "meta-llama/Llama-2-7b"
 BASE_MODEL_PATHS = [BaseModelPath(name=MODEL_NAME, model_path=MODEL_NAME)]
@@ -33,6 +34,16 @@ async def _async_serving_engine_init():
     return serving_engine
 
 
+@pytest.mark.asyncio
+async def test_serving_model_name():
+    serving_engine = await _async_serving_engine_init()
+    assert serving_engine._get_model_name(None) == MODEL_NAME
+    request = LoRARequest(lora_name="adapter",
+                          lora_path="/path/to/adapter2",
+                          lora_int_id=1)
+    assert serving_engine._get_model_name(request) == request.lora_name
+
+
 @pytest.mark.asyncio
 async def test_load_lora_adapter_success():
     serving_engine = await _async_serving_engine_init()
diff --git a/vllm/entrypoints/openai/serving_chat.py b/vllm/entrypoints/openai/serving_chat.py
index 0738210e27cb6..a5e7b4ac3bb30 100644
--- a/vllm/entrypoints/openai/serving_chat.py
+++ b/vllm/entrypoints/openai/serving_chat.py
@@ -123,6 +123,8 @@ async def create_chat_completion(
                 prompt_adapter_request,
             ) = self._maybe_get_adapters(request)
 
+            model_name = self._get_model_name(lora_request)
+
             tokenizer = await self.engine_client.get_tokenizer(lora_request)
 
             tool_parser = self.tool_parser
@@ -238,13 +240,13 @@ async def create_chat_completion(
         # Streaming response
         if request.stream:
             return self.chat_completion_stream_generator(
-                request, result_generator, request_id, conversation, tokenizer,
-                request_metadata)
+                request, result_generator, request_id, model_name,
+                conversation, tokenizer, request_metadata)
 
         try:
             return await self.chat_completion_full_generator(
-                request, result_generator, request_id, conversation, tokenizer,
-                request_metadata)
+                request, result_generator, request_id, model_name,
+                conversation, tokenizer, request_metadata)
         except ValueError as e:
             # TODO: Use a vllm-specific Validation Error
             return self.create_error_response(str(e))
@@ -259,11 +261,11 @@ async def chat_completion_stream_generator(
         request: ChatCompletionRequest,
         result_generator: AsyncIterator[RequestOutput],
         request_id: str,
+        model_name: str,
         conversation: List[ConversationMessage],
         tokenizer: AnyTokenizer,
         request_metadata: RequestResponseMetadata,
     ) -> AsyncGenerator[str, None]:
-        model_name = self.base_model_paths[0].name
         created_time = int(time.time())
         chunk_object_type: Final = "chat.completion.chunk"
         first_iteration = True
@@ -604,12 +606,12 @@ async def chat_completion_full_generator(
         request: ChatCompletionRequest,
         result_generator: AsyncIterator[RequestOutput],
         request_id: str,
+        model_name: str,
         conversation: List[ConversationMessage],
         tokenizer: AnyTokenizer,
         request_metadata: RequestResponseMetadata,
     ) -> Union[ErrorResponse, ChatCompletionResponse]:
 
-        model_name = self.base_model_paths[0].name
         created_time = int(time.time())
         final_res: Optional[RequestOutput] = None
 
diff --git a/vllm/entrypoints/openai/serving_completion.py b/vllm/entrypoints/openai/serving_completion.py
index ee97d35f2b087..b3436773062f3 100644
--- a/vllm/entrypoints/openai/serving_completion.py
+++ b/vllm/entrypoints/openai/serving_completion.py
@@ -85,7 +85,6 @@ async def create_completion(
             return self.create_error_response(
                 "suffix is not currently supported")
 
-        model_name = self.base_model_paths[0].name
         request_id = f"cmpl-{self._base_request_id(raw_request)}"
         created_time = int(time.time())
 
@@ -162,6 +161,7 @@ async def create_completion(
         result_generator = merge_async_iterators(
             *generators, is_cancelled=raw_request.is_disconnected)
 
+        model_name = self._get_model_name(lora_request)
         num_prompts = len(engine_prompts)
 
         # Similar to the OpenAI API, when n != best_of, we do not stream the
diff --git a/vllm/entrypoints/openai/serving_engine.py b/vllm/entrypoints/openai/serving_engine.py
index 63f27b955461e..d5ad4354c78be 100644
--- a/vllm/entrypoints/openai/serving_engine.py
+++ b/vllm/entrypoints/openai/serving_engine.py
@@ -661,3 +661,16 @@ async def unload_lora_adapter(
 
     def _is_model_supported(self, model_name):
         return any(model.name == model_name for model in self.base_model_paths)
+
+    def _get_model_name(self, lora: Optional[LoRARequest]):
+        """
+        Returns the appropriate model name depending on the availability
+        and support of the LoRA or base model.
+        Parameters:
+        - lora: LoRARequest that contain a base_model_name.
+        Returns:
+        - str: The name of the base model or the first available model path.
+        """
+        if lora is not None:
+            return lora.lora_name
+        return self.base_model_paths[0].name