I am not sure why they chose gattaca for the name, but the letters do form the dna base pairs, at, gc, adenine, thymine, guanine, cytosine.
maybe gattaca is a specific gene.
The sequence “gattaca” is too short to be a gene, or even to be a specific DNA element.
Out of curiosity, I tried searching a DNA database for that sequence. I didn’t find anything, which tells me that the sequence is so short that it probably shows up millions (billions? trillions?) of times in the database.
As a curiosity, I once saw a (not very serious) scientific paper describing the DNA sequences seen in Jurassic Park. Those sequences in the movie are real, but they are not from dinosaurs. They are from a common piece of DNA that was developed for genetic engineering back in the 1970s.