Say nothing and avoid repercussions.

Pack-drill was a punishment given to soldiers in the British Army, requiring them to undertake drill (exercise) in full uniform and carrying a heavy pack.

‘No names, no pack-drill’ is used to indicate that the names of those who have committed a misdemeanour will not be mentioned in order to spare them punishment.

The ‘pack-drill’ punishment is known from at least 1845, when it was referred to in William Maxwell’s Hints to a soldier on service:

“A full guard house, dozens at pack-drill.”

The ‘no names, no pack-drill’ mantra is first recorded in a memoir of the Indian Treaty negotiations, which took place between the British and Native Americans in Canada in the late 1860s. This piece from the Manitoba Daily Free Press lists the phrase as an ‘old saw’ (that is, a traditional, homespun proverb) in July 1874:

[Notes taken] At the time of the Indian Treaty of 1873.
No NAMES — No PACK DRILL. — Old saw.