[Facts] This looks like a job for.... Super Anagram-man!
P.L. is the one to ask about anagramming those star names for you, as he's the expert.
I checked my Star Names book for you and, yep, you got all three of those names right. The book offers a few variations on the names, though.
"Alnitak" (the lowest star in Orion's Belt) is also sometimes called "Alnitah". The original Arabic name for this star was: "Al Nitak", meaning "The Girdle".
"Anilam" (the middle star) is also called "Alnilam", "Ainilam", and "Alnihan". The original Arabic name for this star was either "Al Nitham" or "Al Nathm", both meaning "The String of Pearls".
"Mintaka" (the highest star) is sometimes called "Mintika". The original Arabic name for this star was "Al Mintakah", meaning "The Belt".
So, P.L. has a lot of names there to anagram for you! If he can get to it, that is. I only just found out today that his baby daughter Nephele has had a nasty cold all this past weekend and that P.L.'s been getting very little sleep (which may explain some understandable crankiness :)
P.L., if you're reading this, I'm sending a "get well" pressie in the snail mail to you for little Nephele. Nothing big, just a little something that'll look pretty on her. :)
Phyllis, you send little Nephele some positive energy. :)
-- Nanaea