Like all Orthodox Christians, the members of the Imperial Family were named for Saints in the Orthodox Calendar.
Nicholas for St Nicholas of Myra (who has since morphed into Santa Claus in the West) Dec 6/19
Alexandra for St Alexandra the martyr - wife of Emperor Diocletian of Rome who started an extremely bloody persecution of Christians - Alexandra was converted by the sufferings and martyrdom of St George, and if my memory serves me correctly is celebrated on the same day: Apr 23/May 6
Olga for St Olga equal to the Apostles 11/24 July. A Kievan-Rus princess who became Christian. Grandmother (I think) of St Vladimir who baptised the Russian people.
Tatiana for the Martyr St Tatiana of Rome 12/25 January
Maria for St Mary Magdalene, Apostle to the Apostles
22 July/4 Aug. The idea that she was a prostitute is a later western mediaeval notion, not found in Orthodox tradition.
Anastasia for (I think) Martyr Anastasia of Rome 29 Oct/
11 November. There are 4 other Anastasias from the early days of the Church, and it could be for any of them she is named, I am not sure off-hand. If anyone knows GD Anastasia's name day, then I could check and find out which St Anastasia she is named for. Anastasia is the feminine form of the Greek word for Resurrection, which is what her name means.
Alexei for (I think, but can't remember of hand) St Alexis the Wonderworker, Metropolitan of Moscow 12/25 Feb. He is also celebrated on 5/18 Oct with other Metropolitans of Moscow who have been glorified.