The zero watt bulbs as we call it aren’t actually having a power rating of zero watts. These small incandescent bulbs have a power rating of 10-15W.
In the earlier days before the advent of digital meters, energy consumption was recorded using electro-mechanical energy meters.
The energy consumption was recorded by counting revolutions of a disc through mechanical counters. To get the disc revolving there has to be a certain minimum current flowing through the meter. Now the current drawn by these bulbs is very small to get the disc rotating and hence the energy consumption is not recorded by the electro-mechanical energy meters.
So it seemed that these bulbs have no power and hence they got the name zero watt bulb. (Watt is the unit of power).
With the advent of digital meters, even energy consumed by a small 0.1 W LED could also be measured and hence the zero-watt bulb is now a misnomer.