Why are Srivaishnavas averse to give shiva-related names to their children, as others, like even Madhvas (Shiva Rao, Shankaranarayana, Manjunatha, etc. are available among Madhvas), do? Is it because of Periyazhwar's injunction: naaranan tam annai narakam pugaal? (The mother of a child named Narayana will not go to hell). When Srivaishnavas hold all Rudra-related vedic mantras, including Srirudram, to be a prayer to Narasimha, and all names like Umapati, Nilalohita, Nilakantha, Trilochana, etc. refer to Narasimha only, why should not these names be given to their children as the names are legitimately those of Vishnu according to them? Is there any work of Sri Vedanta Desikar that prohibits giving Shiva-related names?
Could be many reasons:
(1) There is an enormous amount of denigration of Siva by Iyengar luminaries like kurattazhwan. This has to influence how they name their children.
(2) Iyengar ideology deems Siva a Jiva - someone who is subject to birth and death like you and me. He is also regarded by them as someone who gets overcome by tamas from time to time. Their Vishnu is considered by them to always show good qualities. this has to influence them.
(3) They undergo Saranagati or Bharanyasam - after which they can only worship vishnu. So they might have an issue with calling their children by Siva-related names after saranagati.
(4) Simple Ajamila effect - they may think they are accruing merit each time they call their child by his vishnu-related name.
It's all a matter of choice. Every family has their own favourite god/goddess. Srivaishnavas are not averse to naming their children by Shiva related names, rather the pool of names from which they can make a choice is filled with a lot of Srivaishnava names. I've seen Srivaishnavas having Shiva related names. It's just that they prefer naming their children by Vishnu related names.
In the end, it boils down to own's choice.
They worshiped their ishta dheivams,so name as like their wish.There is nothing for and against a particular deities. In Tamil Nadu majority of people follow two cultures "Saivam" and "Vainavam" also they do have their favorite deity called as "Ishta dheivam" so that,they naming their child based on their favorite deity irrespective to god or goddess.