fix(provider/openai): remove redundant name from custom tool args

[dancer]

background

followup to #12948. lars feedback: custom tools required a separate name field in args that duplicated the sdk tool key. every other provider tool derives its name from the key automatically. the extra name introduced alias mapping complexity and the resolveProviderToolName extension to createToolNameMapping

summary

• remove name from customTool args schema and type
• use the sdk tool key (tool.name) as the name sent to openai
• remove resolveProviderToolName from createToolNameMapping in provider-utils
• remove alias mapping tests and repro examples
• update docs and examples

before

tools: {
  write_sql: openai.tools.customTool({
    name: 'write_sql', // redundant
    description: '...',
  }),
}

after

tools: {
  write_sql: openai.tools.customTool({
    description: '...',
  }),
}

verification

• pnpm tsx src/generate-text/openai/responses-custom-tool.ts
• pnpm tsx src/stream-text/openai/responses-custom-tool.ts
• pnpm tsx src/generate-text/openai/responses-custom-tool-multi-turn.ts
• pnpm tsx src/stream-text/openai/responses-custom-tool-multi-turn.ts

checklist

• tests have been added / updated (for bug fixes / features)
• documentation has been added / updated (for bug fixes / features)
• a patch changeset for relevant packages has been added (run pnpm changeset in root)
• i have reviewed this pull request (self-review)

[gr2m]

v7 only

[vercel-ai-sdk]

🚀 Published in:

Package	Version
ai	7.0.0-beta.23
@ai-sdk/alibaba	2.0.0-beta.8
@ai-sdk/amazon-bedrock	5.0.0-beta.8
@ai-sdk/angular	3.0.0-beta.23
@ai-sdk/anthropic	4.0.0-beta.8
@ai-sdk/assemblyai	3.0.0-beta.5
@ai-sdk/azure	4.0.0-beta.10
@ai-sdk/baseten	2.0.0-beta.6
@ai-sdk/black-forest-labs	2.0.0-beta.4
@ai-sdk/bytedance	2.0.0-beta.4
@ai-sdk/cerebras	3.0.0-beta.6
@ai-sdk/cohere	4.0.0-beta.4
@ai-sdk/deepgram	3.0.0-beta.4
@ai-sdk/deepinfra	3.0.0-beta.6
@ai-sdk/deepseek	3.0.0-beta.5
@ai-sdk/elevenlabs	3.0.0-beta.4
@ai-sdk/fal	3.0.0-beta.4
@ai-sdk/fireworks	3.0.0-beta.6
@ai-sdk/gateway	4.0.0-beta.15
@ai-sdk/gladia	3.0.0-beta.4
@ai-sdk/google	4.0.0-beta.12
@ai-sdk/google-vertex	5.0.0-beta.17
@ai-sdk/groq	4.0.0-beta.5
@ai-sdk/huggingface	2.0.0-beta.6
@ai-sdk/hume	3.0.0-beta.4
@ai-sdk/klingai	4.0.0-beta.5
@ai-sdk/langchain	3.0.0-beta.23
@ai-sdk/llamaindex	3.0.0-beta.23
@ai-sdk/lmnt	3.0.0-beta.4
@ai-sdk/luma	3.0.0-beta.4
@ai-sdk/mcp	2.0.0-beta.8
@ai-sdk/mistral	4.0.0-beta.4
@ai-sdk/moonshotai	3.0.0-beta.6
@ai-sdk/open-responses	2.0.0-beta.5
@ai-sdk/openai	4.0.0-beta.10
@ai-sdk/openai-compatible	3.0.0-beta.6
@ai-sdk/perplexity	4.0.0-beta.5
@ai-sdk/prodia	2.0.0-beta.6
@ai-sdk/provider-utils	5.0.0-beta.4
@ai-sdk/react	4.0.0-beta.23
@ai-sdk/replicate	3.0.0-beta.5
@ai-sdk/revai	3.0.0-beta.5
@ai-sdk/rsc	3.0.0-beta.24
@ai-sdk/svelte	5.0.0-beta.23
@ai-sdk/togetherai	3.0.0-beta.6
@ai-sdk/valibot	3.0.0-beta.4
@ai-sdk/vercel	3.0.0-beta.6
@ai-sdk/vue	4.0.0-beta.23
@ai-sdk/xai	4.0.0-beta.12