docs: fix mcp config name (better-auth#7067)

Author: himself65

docs/content/docs/introduction.mdx

@@ -69,7 +69,7 @@ Alternatively, you can manually configure the MCP server for each client:
         {
             "$schema": "https://opencode.ai/config.json",
             "mcp": {
-                "Better Auth": {
+                "better-auth": {
                     "type": "remote",
                     "url": "https://mcp.chonkie.ai/better-auth/better-auth-builder/mcp",
                     "enabled": true,
@@ -81,7 +81,7 @@ Alternatively, you can manually configure the MCP server for each client:
     <Tab value="Manual">
      ```json title="mcp.json"
     {
-        "Better Auth": {
+        "better-auth": {
             "url": "https://mcp.chonkie.ai/better-auth/better-auth-builder/mcp"
         }
     }

packages/cli/src/commands/mcp.ts

@@ -15,7 +15,7 @@ interface MCPOptions {
 
 async function mcpAction(options: MCPOptions) {
 	const mcpUrl = "https://mcp.chonkie.ai/better-auth/better-auth-builder/mcp";
-	const mcpName = "Better Auth";
+	const mcpName = "better-auth";
 
 	if (options.cursor) {
 		await handleCursorAction(mcpUrl, mcpName);
@@ -121,7 +121,7 @@ function handleOpenCodeAction(mcpUrl: string) {
 	const openCodeConfig = {
 		$schema: "https://opencode.ai/config.json",
 		mcp: {
-			"Better Auth": {
+			"better-auth": {
 				type: "remote",
 				url: mcpUrl,
 				enabled: true,