The term for an organism with a chromosome designation of 3n is "triploid". Triploidy occurs when an organism has three sets of chromosomes instead of the usual two sets. This can occur due to various mechanisms, such as the fusion of two gametes that each contain a diploid set of chromosomes, or the failure of chromosomes to separate properly during cell division. Triploidy can have various effects on the organism, including abnormal development, reduced fertility, and increased susceptibility to diseases.