Update references from Hugging Chat to HuggingChat (#2066)

* Update references from Hugging Chat to HuggingChat

* Address PR review feedback: revert Examples heading, fix HuggingChat spelling

Author: gary149

docs/hub/spaces-oauth.md

@@ -107,7 +107,7 @@ Basically, you need to:
 ## Examples:
 
 - [Gradio test app](https://huggingface.co/spaces/Wauplin/gradio-oauth-test)
-- [Hugging Chat (NodeJS/SvelteKit)](https://huggingface.co/spaces/huggingchat/chat-ui)
+- [HuggingChat (NodeJS/SvelteKit)](https://huggingface.co/spaces/huggingchat/chat-ui)
 - [Inference Widgets (Auth.js/SvelteKit)](https://huggingface.co/spaces/huggingfacejs/inference-widgets), uses the `inference-api` scope to make inference requests on behalf of the user.
 - [Client-Side in a Static Space (huggingface.js)](https://huggingface.co/spaces/huggingfacejs/client-side-oauth) - very simple JavaScript example.
 

docs/hub/spaces-sdks-docker-chatui.md

@@ -1,6 +1,6 @@
 # ChatUI on Spaces
 
-**Hugging Chat** is an open-source interface enabling everyone to try open-source large language models such as Falcon, StarCoder, and BLOOM. Thanks to an official Docker template called ChatUI, you can deploy your own Hugging Chat based on a model of your choice with a few clicks using Hugging Face's infrastructure.
+**HuggingChat** is an open-source interface enabling everyone to try open-source large language models such as Falcon, StarCoder, and BLOOM. Thanks to an official Docker template called ChatUI, you can deploy your own HuggingChat based on a model of your choice with a few clicks using Hugging Face's infrastructure.
 
 ## Deploy your own Chat UI