Describe the bug

A clear and concise description of what the bug is.

In the function_schema method of the OpenAI Agents SDK, the following line:

func_name = name_override or doc_info.name if doc_info else func.__name__

does not honor name_override when use_docstring_info=False. This happens because of operator precedence in Python. Without parentheses, the expression is interpreted as:

func_name = (name_override or doc_info.name) if doc_info else func.__name__
So when doc_info is None, even if name_override is set, it falls back to func.name.

Debug information

• Agents SDK version: (e.g. v0.0.3)
• Python version (e.g. Python 3.10)

Repro steps

from agents.function_schema import function_schema

def my_func():
pass

schema = function_schema(
my_func,
name_override="CustomName",
use_docstring_info=False
)

print(schema.name) # Expected: "CustomName", Actual: "my_func"

Expected behavior

Even when use_docstring_info=False, if name_override is provided, it should be used for func_name.

Suggested Fix:
Update this line:
func_name = name_override or doc_info.name if doc_info else func.name
To this (with parentheses to enforce correct evaluation):
func_name = name_override or (doc_info.name if doc_info else func.name)