Rather than 'layers', the Roman numerals at Troy actually refer to 'archaeological phases', which often means an:
"... occupation level and all associated features that were created into or from this point in time"
An archaeological phase may actually include several stratigraphic layers on the site. In practice, when talking about a city, phases often refer to iterations of the place over time.
There is no standard in place for labelling these phases, although many 'tell' sites do indeed use Roman numerals as labels.
In practice, it generally depends on the internal standards of the organisation that carried out the excavation (although the government which has jurisdiction over the site may also require that their labelling standards are applied as part of the permission to excavate).
As @MaximusMinimus pointed out in the comments, the same standard was used at Uruk, where the phases are labelled 'Uruk I' to 'Uruk XVIII'. Similar labelling has also been employed at Çatalhöyük (where the sequence is a lot more complex!), and indeed many other sites.
However, other organisations use different labels for phases. One example would be the phases of St Patrick’s Church, Armoy, County Antrim, which was excavated in 2007 (and where the report is conveniently available online!). In that case, the team from Queen’s University Belfast labelled the phases simply as 'Phase 1' to 'Phase 12'.
[It's worth noting that this convention can cause confusion if a site is being excavated ahead of development, where the development project plan (and so, by extension, the project plan for the archaeological works ahead of development) will often also be broken down into 'phases'!]