Plants that if left to self pollinate produce offspring identical to themselves are called

True-breeding plants.

Explanation:

The self pollination in plants that produces progeny with similar characteristics or traits is called True-breeding plant. The parent and progeny both are identical genetically in true-breeding plants. The alleles shared between both offspring and parental plant is also same. The homozygous alleles are present in such organisms. The presence of homozygous alleles mean both alleles are same thus resulting in similar characters. Thus, plants that if left to self pollinate produce offspring identical to themselves are called True-breeding plants.