feat (provider): add name for provider defined tools for future validation (#6838)

## Background

Tool names for provider defined tools were removed in #6815. They are
needed for future validation of the tool setup.

## Summary

Add provider defined tool names back.

## Future Work

Validate that provider defined tools are used with their correct name in
`streamText` and `generateText` requests.

Author: lgrammel

.changeset/brown-geckos-tell.md

@@ -0,0 +1,5 @@
+---
+'@ai-sdk/provider': major
+---
+
+feat (provider): add name for provider defined tools for future validation

packages/ai/core/generate-text/generate-text.test.ts

@@ -1752,6 +1752,7 @@ describe('generateText', () => {
             web_search: {
               type: 'provider-defined',
               id: 'test.web_search',
+              name: 'web_search',
               inputSchema: z.object({ value: z.string() }),
               outputSchema: z.object({ value: z.string() }),
               args: {},

packages/ai/core/generate-text/stream-text.test.ts

@@ -7594,6 +7594,7 @@ describe('streamText', () => {
             web_search: {
               type: 'provider-defined',
               id: 'test.web_search',
+              name: 'web_search',
               inputSchema: z.object({ value: z.string() }),
               outputSchema: z.object({ value: z.string() }),
               args: {},

packages/ai/core/generate-text/to-response-messages.test.ts

@@ -613,6 +613,7 @@ describe('toResponseMessages', () => {
           web_search: tool({
             type: 'provider-defined',
             id: 'test.web_search',
+            name: 'web_search',
             inputSchema: z.object({
               query: z.string(),
             }),

packages/ai/core/prompt/prepare-tools-and-tool-choice.test.ts

@@ -18,6 +18,7 @@ const mockTools: ToolSet = {
 const mockProviderDefinedTool: Tool = {
   type: 'provider-defined',
   id: 'provider.tool-id',
+  name: 'tool-id',
   args: { key: 'value' },
   inputSchema: z.object({}),
 };

packages/anthropic/src/anthropic-messages-language-model.test.ts

@@ -48,16 +48,19 @@ it('should correctly prepare provider-defined tools', () => {
       {
         type: 'provider-defined',
         id: 'anthropic.computer_20241022',
+        name: 'computer',
         args: { displayWidthPx: 800, displayHeightPx: 600, displayNumber: 1 },
       },
       {
         type: 'provider-defined',
         id: 'anthropic.text_editor_20241022',
+        name: 'text_editor',
         args: {},
       },
       {
         type: 'provider-defined',
         id: 'anthropic.bash_20241022',
+        name: 'bash',
         args: {},
       },
     ],
@@ -89,22 +92,26 @@ it('should add warnings for unsupported tools', () => {
       {
         type: 'provider-defined',
         id: 'unsupported.tool',
+        name: 'unsupported_tool',
         args: {},
       },
     ],
   });
   expect(result.tools).toEqual([]);
   expect(result.toolChoice).toBeUndefined();
-  expect(result.toolWarnings).toEqual([
-    {
-      type: 'unsupported-tool',
-      tool: {
-        type: 'provider-defined',
-        id: 'unsupported.tool',
-        args: {},
+  expect(result.toolWarnings).toMatchInlineSnapshot(`
+    [
+      {
+        "tool": {
+          "args": {},
+          "id": "unsupported.tool",
+          "name": "unsupported_tool",
+          "type": "provider-defined",
+        },
+        "type": "unsupported-tool",
       },
-    },
-  ]);
+    ]
+  `);
 });
 
 it('should handle tool choice "auto"', () => {

packages/anthropic/src/anthropic-prepare-tools.test.ts

@@ -16,6 +16,7 @@ export const bash_20241022 = createProviderDefinedToolFactory<
   {}
 >({
   id: 'anthropic.bash_20241022',
+  name: 'bash',
   inputSchema: z.object({
     command: z.string(),
     restart: z.boolean().optional(),

packages/anthropic/src/tool/bash_20241022.ts

@@ -16,6 +16,7 @@ export const bash_20250124 = createProviderDefinedToolFactory<
   {}
 >({
   id: 'anthropic.bashTool_20250124',
+  name: 'bash',
   inputSchema: z.object({
     command: z.string(),
     restart: z.boolean().optional(),

packages/anthropic/src/tool/bash_20250124.ts

@@ -58,6 +58,7 @@ export const computer_20241022 = createProviderDefinedToolFactory<
   }
 >({
   id: 'anthropic.computer_20241022',
+  name: 'computer',
   inputSchema: z.object({
     action: z.enum([
       'key',