Is there a way to define a different baud rate from the ones we are shown in the dropdown menu of the Serial Monitor? I want to define a custom value.
There is no easy way to do so. The list of available baud rates is hard-coded in the Java source of the Arduino IDE. To add a custom rate, you would have to modify the source code and rebuild the IDE.
I suggest you consider using a terminal emulator instead of the serial monitor. On Linux, I like picocom: not a real terminal emulator, but a minimal program that “connects” the terminal emulator you are already using (gnome-terminal, rxvt...) to the serial port. It supports custom baud rates, which it rounds to the nearest rate the hardware can provide. Picocom works on Mac too.
If you are growing out of the Arduino IDE consider swaping to PlatformIO, baud-rate is just one of the many extra things you will get a chance to tweek. If you are on X64 architecture, you can although use eclipse, but I find platformIO bit better for Arduino. Arduino IDE is an OK starter, but to grow you will need to move further.
To add to Edgar Bonets answer, there are many other serial terminals including but not limited to: pyserial (multiplatform),screen (UNIXes), even good old Putty (runs on nearly everything that can blink I believe even on comodore)...