I think that if to of the same festival pet have a egg that egg should have the tag saying it full blood like two
Arctic Storm Griffi having a baby it should say Arctic Storm Griffi offspring or something

Discussed in the thread linked here, also seen by Krinadon, who addressed it:

Link: https://www.sylestia.com/forums/?thread=10350&page=1#8 Author: Krinadon Time Posted: 1/26/2014 at 2:31 AM The term, "Sylesti" as a breed is correct. Originally, we had in mind to have multiple breeds of each species that were elemental based. So there'd be the plain Qitari (Sylesti), a fire Qitari, a water Qitari, etc etc. You could then interbreed all Qitaries of the different breeds. However, as the Site began to grow and things started falling in place, doing that would be near impossible and a ton... TON of work.. so we dropped it. However, the "Breed" has remained (for now). Most likely we'll be phasing it out entirely. Basically, the breed of Sylesti means that the specific pet is from Sylestia. Other breeds would be from other places. But this plan has all but been scratched. As far as the suggestion, I don't think it's something we'll do. It would flood the market with all sorts of these rare special themed pets and water down their significance. When we do revamp the pet profile page sometime in the next couple of months, we'll be sure that the genealogies will display all relevant data - such as if a related pet is themed or not. This should make it very easy to see if an offspring comes from a pure line or not.

edit:
the last paragraph applies to the suggestion.

thank you