Names: Dylan and Blake Tuomy-Wilhoit
Characters: Nicholas and Alexander Katsopolis
Called: Nicky and Alex
Nicky and Alex are Jesse and Becky's twin boys.  They are born into the fifth season of Full House.  The boys are cute from the beginning, fingerpainting on everything, and aspiring to be their cool dad.  It was difficult to tell them apart, but as they grew, they each developed their own character traits.  (Most probably not scripted.)  Nicky is more wild, while Alex is more reserved. 
Blake and Dylan Tuomy-Wilhoit were born on November 29, 1990.  Dylan is older by 19 minutes.  They live in San Fernando Valley in California with their parents, dog (Kuma), cat (Cammie) and turtle (Yertle).  Blake and Dylan were just two years old when they were cast as the Katsopolis kids.  Word has it, John [Stamos] saw their hair and knew that these were meant to be his boys.  The producers were hoping that these twins would take off and be as successful as those other Full House twins, but when the series ended, so did Blake and Dylan's careers.  Blake likes chasing girls, while Dylan is a fan of drawing and painting.  They have just recently begun to go to auditions. 

Full House (1992-1995)
Pictures of the Boys from Full House
I found these recent pictures of the twins.