The Greek classics ones will date, because they are currently trendy. Some of them are a bit try hard.
'Boring' classic names don't date too badly. Cast your mind back about 20 years and names like Ryan and Shannon were popular, but I doubt that many babies are called those names now.
Clusters of similar names tend to be popular. They will date. Gary, Darren, Karen and Sharon give you an idea of their age just from their name.
Names like Sarah, Emily, Emma, David, Thomas and Peter are still quite popular.
I'd suggest you pick a name that is a recognised name but one that you don't hear much of it. For boys, currently names from the Old Testament , vowel-heavy names, and short names are popular (Leo, Theo. Arlo, Ezra, Hugo, Milo...).
Girl names are very samey - either vowel heavy and frilly, or short and with the same consonants. Think Olivia, Aurelia, Aurora, Arabella, Isabella, Ellie, Evie, Eva, Ava,Lily, Luna, Lyra, Lola, Isla, Mia, Maia, May, Mila.
A happy medium might be a name like Marcus, Douglas, Michael or Philip. Not too long, not overused, shorter forms are fine.