Let's talk about the ethnicity of the name "Asyldin". Immediately two things come to my mind.
1) Names on Threnody often include concepts. In this case we have "Asyl" in the name, which is synonymous with Asylum, what might be a pretty common name on Threnody. At least it fits to names like Silence.
2) "-din" (or probably just "-in") is the Alethi particle in names that indicates something like "born from", "born through". There are a couple of names ending with -din, notably Kaladin, Bordin (Dalinars agent), Redin (the heterochromatic Bastard of the jahkehvedan highprince, plus a historical figure named Dandos Heraldin, which is a cameo of Dan Dos Santos. [my Spanish/Portuguese is close to zero, but Dos Santos means something like "of the saints", so Heraldin "of the heralds" is reasonable].
Combining these two, Asyldin might be an Alethi-Threnodite offspring, with "Asyldin" meaning "Asylum's daughter".
Or, she is an Alethi-Terrismen offspring who was born on Scadrial, which her parents considered an Asylum (eg from possible highprince-wars in eastern Roshar), meaning something like "born in an Asylum".
Note: names ending with -din are not uncommon elsewhere in the Cosmere, notably Bavadin and sone characters on Scadrial. No Terrismen, though.