Update name of Genkit (modelcontextprotocol#224)

* Update name of Genkit

This is the updated official name of the library (no brand prefix).

* Update clients.mdx

Author: mbleigh

clients.mdx

@@ -18,7 +18,7 @@ This page provides an overview of applications that support the Model Context Pr
 | [Cursor][Cursor]                            | ❌          | ❌        | ✅      | ❌         | ❌    | Supports tools.                                                             |
 | [Emacs Mcp][Mcp.el]                         | ❌          | ❌        | ✅      | ❌         | ❌    | Supports tools in Emacs.                                                    |
 | [fast-agent][fast-agent]                   | ✅           | ✅        | ✅      | ✅          | ✅     | Full multimodal MCP support, with end-to-end tests |
-| [Firebase Genkit][Genkit]                   | ⚠️          | ✅        | ✅      | ❌         | ❌    | Supports resource list and lookup through tools.                            |
+| [Genkit][Genkit]                            | ⚠️          | ✅        | ✅      | ❌         | ❌    | Supports resource list and lookup through tools.                            |
 | [GenAIScript][GenAIScript]                  | ❌          | ❌        | ✅      | ❌         | ❌    | Supports tools.                                                             |
 | [Goose][Goose]                              | ❌          | ❌        | ✅      | ❌         | ❌    | Supports tools.                                                             |
 | [LibreChat][LibreChat]                      | ❌          | ❌        | ✅      | ❌         | ❌    | Supports tools for Agents                                                   |
@@ -149,8 +149,8 @@ Claude Code is an interactive agentic coding tool from Anthropic that helps you
 - Built in support for "Building Effective Agents" workflows.
 - Deploy Agents as MCP Servers
 
-### Firebase Genkit
-[Genkit](https://github.com/firebase/genkit) is Firebase's SDK for building and integrating GenAI features into applications. The [genkitx-mcp](https://github.com/firebase/genkit/tree/main/js/plugins/mcp) plugin enables consuming MCP servers as a client or creating MCP servers from Genkit tools and prompts.
+### Genkit
+[Genkit](https://github.com/firebase/genkit) is a cross-language SDK for building and integrating GenAI features into applications. The [genkitx-mcp](https://github.com/firebase/genkit/tree/main/js/plugins/mcp) plugin enables consuming MCP servers as a client or creating MCP servers from Genkit tools and prompts.
 
 **Key features:**
 - Client support for tools and prompts (resources partially supported)