Schematic: This does not look like an Arduino Board. How is the schematic related to your questions?
One more thing: You should not connect the LCD to 5V GPIO Pins. You need a level shifter IC (like 74HC4050) between the controller and the display.
Display: A displays usually comes with a display controller. It is a key information to know the controller name. In your case it is a ST7565 (as stated in the datasheet).
Display PCB: The ST7565 supports several communication interfaces (parallel, SPI, I2C). Usually the type of the interface can be changed on the PCB by changing solderbridges there. Please post a picture of the back side of your display to identify the interface type.
Library: This display is supported by u8g2, see here: ST7565R JLX12864-378G V2.0 · Issue #440 · olikraus/u8g2 · GitHub. Use the NHD_C12864 constructor:
u8g2setupcpp · olikraus/u8g2 Wiki · GitHub
Oliver