The term Iyer and Ayyangars,spelled as Aiyer and Iengars as well, are two Brahmin communities in South India.
How these names of these communities came into use?
There is no reference to these communities in the Vedas or the Smrtis.
The Vedas do not provide a distinction between those who worship Vishnu or Shiva,
Those who follow the Vedas are known as Vaidikas, which includes everyone who follows the Vedas.
In this correct sense those who worship Ship Visnu and Shiva or any other God mentioned in the Vedas are Smarthas and Vaidikas (this refers to Brahmin community.
It is suggested in the Smriti that Brahmins use the surname as Sharma, Kshatriyas, Varma and the Vaisyas, Gupta.
There are no other suggestions on this issue.
One can also find , among the Brahmins of the North, to include the name of the profession,or the type of Yaga they performs, like Vajpayee-Those who perform Vajapaya Yaga: then there are others who include the Rishis name,like Kak, to indicate Garga, Gargi.
The concept of surnames do not exist in India.
This has been a recent development.
The custom of keeping the Father’s name in the initial is also recent, say about 200 years, though there is no record of this.
The Smritis have described the elaborate system of identifying one, in the form of Abhivadanam, where the first ancestors,three important lineage, the part of Veda one is practicing, the commentator whose commentary is being followed and one’s name.
One would not find Father’s name here also.
One can find the Grandfathers’ name if the individual is second born;if first-born the Family Deity’s Name will be known.
It is traditional to keep the name of the Family Deity to the eldest child(Male))and paternal Grandfather’s name to the second Male.
Hinduism forbids the disclosure of personal information to all and sundry.
They can be used for Abhichaara Prayoga by vested interests.
Abhivadanam is to be done for elders of the same community and Brahmins and only those who can Bless you with Veda Swasthi Mantra(Blessings from the Veda)
As far as I could check the terms Iyers, Ayyangars seem to have evolved during the middle ages, some say during Ramanuja’s period, though there seems to be no solid evidence on this.
There terms were formulated to build an Endemic group by some.
Unfortunately this is being practiced to-day to divide Hindu Brahmins ans Iyers ans Ayyangars, North Indian Brahmin and a South Indian Brahmin.
These have no sanction of the Vedas nor the Smriti.
Please read my post on Abhivadanam.
However in chaste Tamil Iyan means one who realized the Brahman, one of better upbringing , worthy of respect-no religious connotations are intended .