There are a variety of words that could be used as synonyms for "strong perfume." One possibility is "potent fragrance," which suggests a powerful aroma that might be overwhelming for some. Another option is "intense scent," which could convey both the strength and the depth of the fragrance. "Heavy aroma" is another possibility, evoking a sense of density and richness. "Powerful cologne" could also be used, although it might be more appropriate for male fragrances. Ultimately, the choice of synonym may depend on the context and desired effect, as well as personal preference.