Lot to unpack there....so:
But other than kidding, if your conversation with Tess was exactly as you remembered it, then it makes sense why Delilah calls herself DeKock...We know for a fact that she's not DeKock by blood, but your suggestion that she might be in some way similar to Olivia (in that Cynthia could have been forced to raise her) or that she's just a foster daughter (due to Cynthia's sudden burst of kindness) makes even more sense.
Yeah, maybe slightly different to Olivia (as she does remember elena playing with her) but yes, if she was 'aquired' at a young enough age, then she would never know anything different would she? The bigger question is, as already mentioned, how did Cynthia 'aquire' her? Been discussing this also with Silver, remember Alyssa on the yacht telling Pat that Charlotte was the head of one of the 'big seven families' in New Paris? I'm going out on a limb, but I'm thinking she may be from one of those other families...even possibly a Richelieu...
Silver has shown though with his above screenshots, that she is unaware and can find out...so...we shall just have to wait and see. The more I think on it though the more I'm convinced (given what Cynthia is like and what Phoebe says to both Yvette and Elena about her) that Delilah was probably 'taken'...bargaining piece...debt...whatever.
Cynthia could very well have given her that last name, since it doesn't obligate her to anything, given that her true heirs by blood are her children Stefan and Nadia. But the DeKock surname would give Delilah the feeling that Cynthia sees her as her child, not just a foundling (even if Delilah is not a foundling, but, say, the daughter of some important person)...
Nadia seems unlikely to be hers...her niece though definitely. Again, this is something that is still not confirmed 100% but Tess never actually corrects anyone but reading between all the lines and connecting the numerous dots, she is most likely Cole's daughter...(though in my own sheet, I do still have most of the relations greyed out, as I always will until 100% confirmed in story). Who with...also remains to be seen or stay forever a mystery. We do seem to have a lot of missing never-talked-about parents in KG lol.
Besides, the Karlssons don't need to know that Cynthia sent not Delilah DeKock, whose surname automatically grants a lot of privileges and even protects its bearer, but just some girl who was brought up by her, not belonging to the elite, to spy on them. (I'm not sure about the latter, though, and I think the Karlssons may well know the whole truth about Delilah).
You could be on to something here for sure. We circle back around to the who and where but a potential spy? Very possibly, even likely (originally) perhaps. Do the Karlsson's know who she really is? Again, also possibly given their respources etc etc. Tess says in Silver's other screenshot that she can potentially 'move'. Move? Move faction...desert the DeKocks? Who actually already knows for Delilah to 'find out'? Pretty sure no one in the DeKocks will give that info up freely....