Build name customisable

I am evaluating Artifactory for TeamCity(version 8.06) for my project

When an artifact is saved to Artifactory from TeamCity, the build name is defaulted to the TeamCity path. Is this customisable?

We like to retrieve the latest artifact from TeamCity and to my knowledge we need the build name to accomplish this. Hypothetically if we move or rename the project we would lose the reference to it in Artifactory, as it is using the TeamCity path as the build name.