* Purebred: This term is used more commonly for animals and plants, but it implies the same concept as homozygous - having two identical alleles for a trait.
* Identical genotype: This is a more technical way of saying homozygous, focusing on the genetic makeup rather than the breeding history.
* Having two identical alleles: This is a more literal description of the homozygous condition.
* True-breeding: This term is used when describing organisms that consistently produce offspring with the same traits, which is a result of being homozygous for the relevant genes.
Ultimately, the best alternative depends on the specific context of your writing.