The Linnaean classification system classifies and groups organisms into taxonomic groups: Kingdom, Phylum, Class, etc. Obviously, a clade at any taxonomic level is uniquely determined by its classification at this level and all its parents in the hierarchy, e.g., Kingdom = Bacteria, Phylum = Firmicutes, Class = Clostridia uniquely identifies a group of bacteria. But is this group also uniquely identified by just Clostridia? Or are there situations where two Phylums might both contain Classes with the same name?
Since Genus & Species are typically used to identify organisms, I would assume that combinations of these at least are unique. As @Jam pointed out in the comments, Species alone is not enough. Note, however, that I am not asking about the binomial name for a species - I am asking about uniqueness among higher levels of aggregation, such as Class, Order, and Family.