Atmega328p with arduino without the board
The board option is actually selecting a variant out of the installed cores (which provide the basic Arduino framework for a group of boards/chips). Each core can support multiple variants/boards/chips and can give each of them individual lists of options. There certainly also is a core, which supports the Atmega328p with all needed config options (like the frequency setting). You just need to install it from the boards manager.
Though, since you use a 16MHz crystal just like the Uno/Nano, you could just select the Uno or Nano as board. Neither the Arduino IDE, nor the Atmega328p can know, that the Atmega is actually a standalone one and not mounted on an Arduino board. So you can just use that board when you keep the config options inherent to an Arduino Uno/Nano (frequency setting and pin mapping mainly).