Lieutenant Commanders are properly addressed as "Commander" but this is probably an oversight, it should be noted that both Tuvok's and Tom Paris' ranks were retconned late in season one. It's possible that they forgot to fix Chakotay's rank.
- Only sometimes is this informal abbreviation used, even on the show. It's hard to believe that they made the same oversight for seven whole seasons when they managed to fix it on other characters pretty early on; not to mention that somebody in the costume department would have noticed when swapping his rank for "real" Lt. Comander pips in "In the Flesh". I suppose maybe they did notice and didn't feel like making a new insignia pin?
There is also the fact that Chakotay and the rest of Voyager's Maguis crew are not registered starfleet officers so in a manner of speaking he isn't a starfleet lieutenant commander or commander
It's most likely just a costuming screw-up that never got corrected. Aside from the rank insignia, he was always referred to as "commander," even in writing. It's interesting to note, however, that the officer he replaced was a lieutenant commander.
Much as we fans would like to have a consistent story, TV shows are put together by a huge crowd of people who are sometimes working at cross purposes. That often leads to inconsistencies. I think that's how Chakotay ended up having one rank but wearing the insignia of another.
Here's my theory: somebody decided that it was lame that all Star Fleet commanding officers have the same rank. That doesn't happen in real-world navies, where bigger vessels have higher-ranking commanding officers. Only the biggest warships have "captains" whose actual rank is Captain. In the U.S Navy, a destroyer is typically commanded by a Commander. That person may be addressed as "Captain" but that's a title, not a rank. The first officer is typically a Lt. Commander.
Now, when they were inventing the imaginary starship Voyager, they could have decided that it was the Star Fleet equivalent of a destroyer, with CDR Janeway as CO and provisional LCDR Chakotay as XO. Then somebody else came along and decided having Janeway both a "Captain" and a "Commander" was too confusing. Mass media hates confusing details, and so that person won the argument: Janeway had to be a Captain, period. To be consistent, her XO had to be a Commander.
At this point they could change Janeway's insignia just by attaching another pip. But giving Chakotay a new rank insignia would have meant manufacturing it. If they were just about to start shooting, there wouldn't have been time.
I also believe that something like this happened when Roddenberry was putting together TOS. Note that Kirk's sleeves have two solid lines with a broken line in between. That looks suspiciously like a futuristic version of the USN insignia for a LCDR. Furthermore, he addresses Spock as "Mister". Perhaps Star Fleet customs are different, but in the USN a "Mister" is a LCDR or lower. So probably Roddenbery originally meant for the Enterprise to be the future equivalent of a Destroyer or Frigate. But that would have been too confusing
Actually, they intentionally designed the rank insignias with fewer braids then the equivalent Navy rank in an effort to make it look different and more futuristic, this is also why Ensigns have no braids at all. It is definatively established that Kirk's rank is Captain, it's not just a title. My guess as to why Chakotay's rank doesn not match his insignia is they wanted him to be an LCDR like Cavit, but then forgot about it and never bothered to fix his pin. If you are interested, there is an extensive debate on Chakotay's Talk Page on Memory Alpha.-Cpthunt (talk) 05:09, August 14, 2013 (UTC)