Function output have normal tool name without final_result_ prefix

[BeautyyuYanli]

Following #1785 , I want the function output behave with the same name as normal tools, i.e. hand_off_to_maths_agent instead of final_result_hand_off_to_maths_agent.

[BeautyyuYanli]

@DouweM Waiting for your review :)

[DouweM]

@BeautyyuYanli Pydantic AI already lets you specify a custom tool name by using output_type=[ToolOutput(hand_off_to_maths_agent, name="hand_off_to_maths_agent"), ...] instead of output_type=[hand_off_to_maths_agent, ...]. Can you give that a try?

If you think we should change the default behavior, I'd suggest filing an issue as it would require a bit more thought and discussion, since the final_result prefix also serves as a bit of a hint to the LLM that it's not a regular tool call, but one that will end the conversation.

I'll close this PR for now, also keeping in mind that it'll end up conflicting with #1628 which we'll be merging soon.