で is the ~te form of です.
one use of the ~te form is that it can be used to combine two small clauses to make a compound sentence. In this case,
Japanese
男の子の名前はツコウで、女の子の名前はキャカでした。
Romaji
otoko no ko no namae ha tsukou de, onna no ko no namae ha kyaka deshita.
English
The boy's name was tsukou, and the girl's name was kyaka.
The use of "deshita ga" would be like "however," or "but." It is used to combine clauses but not the same way as "and."
男 (otoko) means man, 女 (onna) means woman, and 子 (ko) means child. so 男の子 is boy and 女の子 is girl.