Sasha
[name_f]Sadie[/name_f]
Siddalee is one of my favourite S names.
Other names that I think fit the gender neutral theme
[name_u]Sutton[/name_u]
[name_u]Sloane[/name_u]
[name_m]Slater[/name_m]
[name_u]Skipper[/name_u]
[name_m]Scully[/name_m]
[name_u]Skylar[/name_u]
[name_u]Salem[/name_u]
[name_u]Shannon[/name_u]
[name_u]Sasha[/name_u]
[name_u]Sammy[/name_u]
[name_u]Sheridan[/name_u]
My name ([name_u]Skyler[/name_u]) firs your criteria perfectly! ^.^
My personal favorites are [name_u]Shea[/name_u]/Shay, [name_u]Shiloh[/name_u], & [name_f]Sunday[/name_f]. [name_f]Sedona[/name_f] is a really cute name tho.
Senna
[name_u]Shay[/name_u]
[name_u]Skye[/name_u]
[name_u]Shiloh[/name_u]
Saffron
[name_u]Sorrel[/name_u]
[name_f]Saphira[/name_f]
[name_f]Sappho[/name_f]
[name_f]Sapphire[/name_f]
[name_u]Sandy[/name_u]
[name_f]Sandra[/name_f]
[name_f]Stella[/name_f]
Saige, [name_f]Sophie[/name_f], and [name_f]Sienna[/name_f]
My favourite S name is actually [name_f]Savannah[/name_f] 
! I also love [name_f]Sylvie[/name_f] and [name_f]Summer[/name_f] but I don’t think either fits your style.
Maybe…
[name_u]Sutton[/name_u]
[name_u]Sailor[/name_u]
[name_u]Sierra[/name_u]
[name_f]Solene[/name_f]
[name_f]Sunday[/name_f]
[name_f]Saskia[/name_f]
[name_u]Sheridan[/name_u]
[name_u]Shiloh[/name_u]
[name_u]Sydney[/name_u]
[name_u]Skylar[/name_u]
And for what it’s worth I think [name_u]Sunny[/name_u] could be a full name on it’s own!
Salem
[name_u]Sasha[/name_u] / [name_u]Sascha[/name_u]
Sailor
[name_u]Skyler[/name_u]
[name_f]Selah[/name_f]
[name_u]Sutton[/name_u]
[name_f]Soleil[/name_f]
[name_u]Sierra[/name_u]
[name_f]Suri[/name_f]
[name_f]Sarai[/name_f]
Sunniva
[name_u]Skyler[/name_u]!
[name_f]Samiya[/name_f]
[name_u]Sanya[/name_u]