"Tatiana" was not by any stretch of the imagination a "royal name" in imperial Russia, not at least until the very last decades of that empire, when two grand duchesses were bestowed with it. Indeed, for most of imperial Russian history "Tatiana" was a name associated with the peasantry. Of course, in the 1830s, Pushkin made it famous as the name of the heroine in his novel-in-verse, Eugene Onegin, but there he quite pointedly makes fun of the fact that he has given his noble female protaganist such a commonplace, indeed, some would even say vulgar name. Obviously, at this time the name "Tatiana" was not exactly comme il faut among Pushkin's peers in the Russian gentry and aristocracy.
It's interesting how this still lingers on in some environments. Perhaps not with regard to the name Tatiana, but the nickname Tanya or Tanja. Here in Norway I'd say this name is associated with white trash, reality stars, teenage single mothers, semi-prostitutes etc. As such it's not a direct import from Slavic-speaking countries, but mainly from American pop culture, perhaps also with a little Gypsy / Romani influence / romance thrown in.
Olga used to be the exact opposite - indicating some older, dignified, yet eccentric lady. (Much like "Agatha" in the Anglo-Saxon world.) This mostly due to the name becoming popular in Norway in the bourgeoisie when Scandinavian royals started marrying Romanovs and then slowly dying out, untill revived by the influx of East European immigrants during the last 25 years, so that the younger generations will probably not think of "Olga" as an old, intimidating aunt persona, but as an immigrant from Eastern Europe.
Interestingly the same trend with a name fashion based on a Slavic name can be seen in the name of Norway's current queen Sonja, nickname of Sophia. The Sonja craze was of course started by Norwegian celebrity figure skater Sonja Henie, born 1912, to a father who was a furrier and thus obviously aware of Russia, perhaps even with Russian business partners.
