At one time I did quite a bit of research on Barlow. Certainly one of the best battlefield Generals in the Union's service. I find the nickname interesting as a result but wish I better understood the origins (if any) and intent.
Not sure of the origins of Dogberry (although I can speculate), but I'm pretty sure of the intent.
The men of the 153rd PA despised Barlow, most likely because they sensed his xenophobic dislike of the Germans under his command.
I have an original (1863 copyright) regimental of the 153rd, worm-eaten and worn, entitled 'Ten Months with the 153d Penn'a Volunteers,' co-written by William Simmers and Paul Bachschmid, a couple of lieutenants in the regiment.
On page 26, they write in the aftermath of Chancellorsville:
"Upon the recommendation of the board of survey, convened to ascertain the kind and quantity of property lost by the men, requisitions were at once made to cover the deficiency, and in less than 10 days the wants of the men were again supplied. This attended to, things began to look more cheerfully. The despondency of the men gradually vanished, and soon all traces of our late disaster were obliterated. With Colonel Glanz in our midst, and Brigadier-General Barlow banished to the Antipodes, our happiness would have been complete. Neither, however, came to pass; Col. Glanz continued in 'durance vile,' Billy Barlow continued the scourge of the division until a chance bullet at Gettysburg lowered the petty tyrant from his exalted position, and freed the division of his presence. The short reign of this individual forms an epoch in our history, which will never be forgotten by those who had the misfortune to serve under him. As a taskmaster he had no equal. The drudgery imposed upon the regiment by the division commander during our sojourn at camp near Potomac Creek Bridge, left the men with little time for recreation. On the morning of the 3d of June, our stay here terminated by the removal of the regiment to camp near Brooks' Station. Here Dogberry ruled, as it were, with a rod of iron, and by his trifling punctiliousness caused everybody 'to be down' on the service."
In addition to the dictionary definition I previously offered for 'dogberry,' the name also shows up as a character in Shakespeare's 'Much Ado About Nothing.' Dogberry is the grand constable of Messina's night watch and represents the jester, fool, or comic relief in the play, particularly with his use of malapropisms.
Wikipedia says 'The name Dogberry reflects Shakespeare’s common practice of giving fools ridiculous-sounding names.'
Double ta-dahh.