Krishna now explains the meaning of his own title. I have gone beyond the perishable — so I am not merely kshara. I am greater even than the imperishable — so I am not merely akshara either. Because I transcend both, I am known in the world and in the Vedas as Purushottama, the Supreme Person.
In a family, there is often one elder who everyone looks up to — the one who holds the family together, the most respected, the most loved. Among all categories of existence, Purushottama holds that place. The perishable world looks up to him. Even the imperishable finds its meaning in him.
This shloka closes the triad that began at 15.16. The framework is complete: kshara is known, akshara is known, and now the one who stands above both is named and explained. Purushottama — the name that gives this entire chapter its title.