Yes the library is correct. You can also experiment with different constructors, there are many (just copy-pasted some HW SPI versions from a library example):
// Please update the pin numbers according to your setup. Use U8X8_PIN_NONE if the reset pin is not connected
//U8X8_SSD1306_128X64_NONAME_4W_HW_SPI u8x8(/* cs=*/ 6, /* dc=*/ 4, /* reset=*/ 12); // Arduboy (DevKit)
//U8X8_SSD1306_128X64_NONAME_4W_HW_SPI u8x8(/* cs=*/ 12, /* dc=*/ 4, /* reset=*/ 6); // Arduboy 10 (Production, Kickstarter Edition)
//U8X8_SSD1306_128X64_NONAME_4W_HW_SPI u8x8(/* cs=*/ 10, /* dc=*/ 9, /* reset=*/ 8);
//U8X8_SSD1306_128X64_NONAME_3W_HW_SPI u8x8(/* cs=*/ 10, /* reset=*/ 8);
//U8X8_SSD1306_128X64_VCOMH0_4W_HW_SPI u8x8(/* cs=*/ 10, /* dc=*/ 9, /* reset=*/ 8); // same as the NONAME variant, but maximizes setContrast() range
//U8X8_SSD1306_128X64_ALT0_4W_HW_SPI u8x8(/* cs=*/ 10, /* dc=*/ 9, /* reset=*/ 8); // same as the NONAME variant, but may solve the "every 2nd line skipped" problem
//U8X8_SH1106_128X64_NONAME_4W_HW_SPI u8x8(/* cs=*/ 10, /* dc=*/ 9, /* reset=*/ 8);
//U8X8_SH1106_128X64_VCOMH0_4W_HW_SPI u8x8(/* cs=*/ 10, /* dc=*/ 9, /* reset=*/ 8); // same as the NONAME variant, but maximizes setContrast() range
//U8X8_SH1106_128X64_WINSTAR_4W_HW_SPI u8x8(/* cs=*/ 10, /* dc=*/ 9, /* reset=*/ 8); // same as the NONAME variant, but uses updated SH1106 init sequence
//U8X8_SH1106_72X40_WISE_4W_HW_SPI u8x8(/* cs=*/ 10, /* dc=*/ 9, /* reset=*/ 8);
However since your display does not have a CS pin and the SPI bus is shared with ADC, there might be a conflict between display and ADC. My display has 7 pins, including CS