Pretty late to the party here, but figured I'd throw my 2 C-Bills in anyways... :))
So, in my opinion, there's a couple of factors to consider here. One thing that influences the CO's rank is the size of the unit - is it a lance, a company, etc.? If it's the unit is only a lance, I can see a mercenary CO inflating his rank to Captain. This elevates the CO a bit on the command ladder, providing him with more control over his forces in a military setting. After all, even if the guy should technically be a lieutenant, having such a low rank technically means that even a Captain can order you around and expect compliance. By taking the rank of Captain, your CO then becomes the 'equal' of the employer's company commanders, and therefore 'technically' has more say over how his unit is used.
Notice that I use the term technically quite a bit in the above statement. The exact limits of what can and can't happen depends a lot on the stipulations of the contract. However, with what I said above in mind, I'd generally take the rank of Captain for forces running from a lance to a company.
If you're running a company, Captain is the rank most commonly used. However, taking the rank of Major could apply the same benefits as above. However, it could also have employers (and their troops) thinking you're CO is rather jumped up and self important - could make for some interesting roleplay scenarios, though.
Another thing to consider might be if the CO served in a regular military before going merc, and if so, what rank did he gain in that time? If he was only an enlisted man, then house troop officers may consider him some kind of idiotic, jumped-up peasant and react badly to any officer rank he takes. If, on the other hand, he achieved the rank of Major and now commands a mercenary company, it may be reasonable for him to use his former rank - even if it is higher than the norm for a company commander, it would likely be considered a show of respect for the position he previously held.
In the end, this all conjecture based off of my own opinion, but I hope it helps.