I am adding some explanation to @Babak answers.
In your current code, you are passing an event handler (handleOnChange) to the onChange onEvent attribute of the Select component.
<Select
.....
onChange={handleOnChange}
/>
When the onChange event happens it will then call the function handleOnChange with the event as default parameter and other parameter
In your expected code, you are passing the result of the handleOnChange(index) function (because of parenthesis we are saying it make a function call and the result is passed to the onChange attribute), but this is not our intention. We have to pass the event handler to onChange attribute not the result of it. That is the golden rule of the event handler in REACT.
If you want to pass arguments other than the event argument then you need to do:
<Select
....
onChange={(value, options) => handleOnChange(value, options, index)}
/>
Here you can see that we are passing a callback function. Note that in the above snippet we cannot access the event inside the handleOnChange. If you want to have an event in the event handler along with other parameters you can do like this:
<Select
.....
onChange={(event, value, options) => handleOnChange(event, value, options, index)}
/>
Some valid event handlers:
<button onClick={handleClick} /> // valid and can access event
<button onClick={() => handleClick()} /> // valid and access event
<button onClick={(event) => handleClick(event, name)} /> // valid and access event and other parameters