These are some of the origins of the girls' names that I have come across in my readings. Perhaps some of you have other possibilities or concrete conclusions:
Olga and Tatiana: Most of what I have read states that these girls were named after the main female characters in Pushkin's novel Eugene Onegin, a favorite of the Imperial couple's. The book Nicholas II: The Imperial Family states that Grand Duke Konstantin Konstantinovich heard this explanation from the Tsar himself. If Nicholas thought he would have another girl, then naming the first Olga so he could name the second Tatiana after these characters would make sense, but then again he could also have had only sons after Olga, thus naming her simply for that purpose wouldn't make much sense. I think a more accurate explanation is that, as I have read, Nicholas liked the name Olga because it was an ancient Russian name.
I also recall reading elsewhere that Olga was named after Nicholas's sister Olga, as that was his favourite sister. Yet I have also read that Xenia was his favourite sister, so I am not too sure about the veracity of this explanation.
Tatiana was said to have been a very popular name choice with the common people, as it was a name used much amongst them and not so much amongst the nobility, so they felt a special affinity towards her.
I don't know whom Maria was named after, although I seem to recall reading that she was named after her paternal grandmother.
Finally, I have read two different explanations regarding whom Anastasia was named after, the first being the most popular. That is that she was named after the Montenegrin princess who was Alexandra's close friend at the time; she was also the same person who first introduced the Tsarina to Rasputin. The other explanation comes from M. Eagar's memoirs Six Years at the Russian Court, where she states "Anastasie means 'the breaker of chains,' or 'the prison opener' [...] The little Grand Duchess was called by this name because, in honour of her birth, the Emperor pardoned and reinstated the students who had been imprisoned for participating in the riots in St. Petersburg and Moscow during the winter." This is the only such explanation I have heard about this, however, and I have also read that Anastasia means "she who will rise again" and not "the breaker of chains," so I am unsure about how accurate this particular explanation may be.