Closest relatives
Names in the same family
Silvia is the direct base form behind Hungarian Szilvia. Sylvia is the familiar English variant, Sylvie is French, and Sylwia is Polish. These are the strongest “similar name” suggestions because the connection is linguistic, not merely stylistic.
Hungarian names with a similar feel
For someone who likes Szilvia because it feels distinctly Hungarian, consider Zsófia, Eszter, Ildikó, Réka, Katalin, Ibolya and Boglárka. They vary in origin, but each has established Hungarian use or form.
Nature-linked alternatives
Because the Silvia family is associated with the Latin forest root, names such as Ibolya (“violet” in Hungarian), Flóra, Willow, Hazel and Sylvan may appeal to someone drawn to the woodland aspect of Szilvia.
Similar in sound rather than origin
Olivia, Livia and Vivia/Vivian share some sounds with Szilvia but do not share the same etymology. That distinction matters: sound-alike is not the same as related name.