Here is a quick script you can put in the Custom content of the Person search screen. This will trim leading and trailing spaces from any text entered into the fields.

I have to paste a screenshot as it wouldn't let me add code :-(

That will stop you when typing in a name that has an actual space.

You could trigger the trim() only if the space key has not been hit:

crm.ready(()=> {
    $('#pers_firtname').on('keyup', (e)=> {
        // trim only if spacebar not hit.
        if (e.keyCode != 32) {
            $('#pers_firtname').val($('#pers_firtname').val().trim());
        }
    });
    // ...
});

That will stop you when typing in a name that has an actual space.

You could trigger the trim() only if the space key has not been hit:

crm.ready(()=> {
    $('#pers_firtname').on('keyup', (e)=> {
        // trim only if spacebar not hit.
        if (e.keyCode != 32) {
            $('#pers_firtname').val($('#pers_firtname').val().trim());
        }
    });
    // ...
});