Why is Lord Vishnu's avatar 'Narasimha' more popular in South Indian region? I've seen in many movies and even when I went to south cities, they name their shops and business on the name Narasimha? Why Narasimha is more popular there?
We can get an astrological connection from the Brihat ParAshara Hora ShAstra, which is one of the most authoritative Jyotisha texts.
This text links each of the Navagrahas with an incarnation of Lord Vishnu as follows:
3-4. The unborn Lord has many incarnations. He has incarnated, as the 9 (Nava) Planets to bestow on the living beings the results due to their 10ths. He is Janardana. He assumed the auspicious form of Planets to destroy the demons (evil forces) and sustain the divine beings.
5-7. From Sun came the incarnation of Rama, from Moon that of Krishna, from Mars that of Narasimha, from Mercury that of Buddha, from Jupiter that of Vamana, from Venus that of Parashurama, from Saturn that of Kurma (Tortoise), from Rahu that of Varaha (Pig) and from Ketu that of Pisces (Fish) occurred. Incarnations other than these also are through the Planets.
Now, it is well-known that the direction that is owned by Mars is the South. So, here we get an astrological clue as to why Narasimha might be more popular in the South as opposed to say in the North (a direction which is ruled by Mercury or Budha and who and Mars are Ati Shatru or great enemies).
A similar argument can also be produced for explaining why Lord KArthikeya is more worshiped in South India. KArthikeya is known to be the over ruling Deity of Mars.