BookingDates::where('email', Input::get('email'))->orWhere('name', 'like', Input::get('name'))->get()

select * from booking_dates where email='my@email.com' or name like '%John%'

BookingDates::where('email', Input::get('email'))
    ->orWhere('name', 'like', '%' . Input::get('name') . '%')->get();

BookingDates::whereRaw('email = ? or name like ?', [$request->email,"%{$request->name}%"])->get();