In the CURL introduction in Chapter 6, there is the mention -O <filename>, but curl takes an output file name as the argument when the option -o.
In addition, if you want the output filename same as the remote, you need the -O option, which doesn't take a filename. While there is explanation that "If you omit the filename argument", the -o option must need a filename, and you cannot add a filename with the -O option, and therefore there is no concept of 'omit' here.