SUDOKU

SUDOKU is not a proprietary name, in other words it does not belong to anyone, any more than the game itself does. Your question is like asking "can I make my own chess sets?" to which the obvious answer is yes. In addition Sudoku has many variants so that it is hard to image that Sudoku could apply only to one product. Go for it.

Just as an FYI: If you search for the trademark "sudoku" on the United States Patent
and Trademark Office (USPTO) web site, you'll find that there are
recent, pending applications for "SUDOKU" (serial number 78658217) and
"SUDOKU DELUXE" (serial number 78653266) in categories such as
"computer game programs." You can find some details about the
application by clicking the serial number, word mark, or "Live," and
further details by clicking "TARR." Searching the US copyright site, I did not find a copyright registration for SuDoku products though registration is not required. So it may depend on how you plan to distribute the puzzles and the manner or form that puzzles may take even though the word and game concept itself may be in the public domain.