The machines do whatever is efficient.
They "tend to count from zero" in our world because in the situation they count this is more efficient. In other situations, it may or may not be efficient to "reserve" the 00 for something else.
Even if they do not reserve it, where is the proof that machines use this name for their city internally? Maybe the name was made for humans (or maybe not). Also, Neo refer to it as "the machine city" instead.
Or maybe had not built another city before 01, maybe they refer to their life with the humans as "the initial state", 00. As often it is necessary to create a prototype to build a stable software from the ground-up afterwards (kind of "wiser after the event"), the machines may have seen their co-living with humans as a prototype of their existence, and gone to fix it's shortcomings into their "release city", 01 (incrementing the version number).
Either way, I find the interpretation of "the first" in 01 a human thing to do, machines most likely interpreted it differently. The nice symbiosis in this is, that while for humans 01 means "first", since, from a human point of view, this is the "first" city of its kind, being a machine city; from a machine point of view, it means (in human terms) "the second one". Most likely because they interpreted their living with the humans as their initial one (and in particular something that didn't work or needed a redesign).
It is very worth to note that after founding their own city and nation, the machines acted in attempt to coexist with humans: they produced vehicles for them for instance. From this point of view, it is not sure that they meant to name the city 01, they could mean "our way of life", as in "our way of life with humans as a dominant part of the environment, version 2.0" (01 in machine terms). But machines... doesn't waste bytes with storing all this and call it just 01. :)