The name "Betzaida" appears to be a Hispanic development of the word "Betsaida", which is Spanish for "Bethsaida", the name of a city mentioned in the Christian New Testament. Three of the apostles were from Bethsaida: Philip, Andrew, and Peter. Bethsaida is also where Jesus is said to have healed a blind man. The name itself means "house of fruits", implying abundance and prosperity.
The name "Yamilka" has posed a problem on this board in the past:http://www.behindthename.com/wwwboardarc/messages/2760.html
Some say that it is another form of "Yamila" or "Jamila", which is Arabic meaning "beautiful". I have no verification that this is the actual origin of the name, though.