The SPI bus progressed to the names MOSI and MISO, by Motorola I think, from the original SPI bus names DIN and DOUT or such like, meaning 'Data In' and 'Data Out'.
It is very often (frankly, call it always) very confusing to use the words IN/INPUT and OUT/OUTPUT in signal names. Directions depend upon where you're looking at a circuit.
Consider an SPI bus between a microcontroller (MCU) bus master and an EEPROM bus slave. Serial data is received by the MCU on a pin formerly known as DIN. The EEPROM manufacturer could either (a) call the EEPROM's serial data output DOUT and rely on the designer to make a cross-over, connecting MCU-DIN to EEPROM-DOUT, or (b) call the EEPROM's serial data output DIN so the designer can connect MCU-DIN to EEPROM-DIN and have no cross-over but pin names that say the opposite of what they mean.
Neither of these would be clear and unambiguous on a schematic without additional information (notes/arrows on schematic, referring to data sheets).
The names Master-Out/Slave-In (MOSI) and Master-In/Slave-Out (MISO) are clear and definitive, solving this problem. They still contain the forbidden-ish 'In' and 'Out' but they state directions for both ends of the wire so the function remains clear.
Incidentally, there are plenty of SPI slave devices with DIN(output)/DOUT(input) pin names kicking about. And every time I see one, I have to reach for its data sheet to check very carefully! :-) I've never had to with the MOSI/MISO scheme.