Frame shift. Why should we care? Picard is a quite common French name, coming in at #81 currently, with 37k out of 60m French people. i.e. about 1/1600, in current France. It was probably higher in the past.
Picard is also an old French name, coming from the inhabitants of Picardie, a region in France that... sits on the English Channel.
In the US, #81 puts you at Ross - 80, Foster - 81, Gomez -82.
Was there really a Mr. Ross at Waterloo? A Mr. Foster at Trafalgar? How would that be a history question?
My probability-fu is rather outdated, but I suspect this is a variation of the shared birthday at a party problem.
(It is not the same problem, but it does boil down to calculating the probability that not a single person is named Picard, which is similar and uses the same reasoning of proof-by-opposite condition often found in probability problems).
If you have 1 officer, the probability that that 1 officer is not named Picard is (1 - 1/1600) is 0.999375. If you have 2 officers, the probability the 2nd one is independent, so the overall probability that neither is named Picard is the 0.999375 x 0.999375. I.e. .999375 to the nth power.
At 200 men you have an 88% probability no one is named Picard, at 500 73% probability. At 1000, 53% and at 2000 men there is only a 28% probability that no one is called Picard.
If I instead use a 1/1000 frequency (before immigration in France, taking into account location of Picardie region compared to a naval battle in the Atlantic) we already have a 40% likelihood of a Picard at 500 count.
Even without looking at detailed data, given the overall troop count there is a very low probability no one called Picard would have participated at Trafalgar.
Am I moving the goal posts by now talking about troops rather than high officers? The top answer here talks of a matelot, pretty much the lowest naval rank. And of another, quarter master, being a senior non-com rank.