User blog comment:DiegoAnime3000/Why they have different last names? Answer found here./@comment-69.117.13.82-20140725043949

Well, there may not be a specific naming tradition in vytal. It's possible that each family decides how to pass along the name. One couple may decide to keep their own surnames, while another may choose one. In the same way, children's surnames could be decided based on each couple's agreement, and the method may not carry over to every child. Therefore, basing this off of the naming conventions of other families is not reliable.

Anyway, we know they are half-sisters, thanks to Monty's confirmation. We can pretty much assume that both share a father as well, as when Ruby and Yang were preparing for initiation, Ruby complained to Yang that she "sounded like Dad". As she does not clarify "your dad" or "my dad", it is most likely that they share a father.

As far as Ruby's family goes, we know that her mother is Summer Rose, and that she has an Uncle named Qrow. Qrow himself is a mystery, as the term "Uncle" is often used in different ways. He may be Ruby's uncle by relation to one of her parents, or Ruby may only refer to him as Uncle due to being a close family friend, or due to the time they spent together while he trained her with the Crescent Rose.

On to the theory itself, assuming that Ruby and Yang have different mothers, this leaves a number of possibilities. Yang is 17, and Ruby is 15. This means that Yang was born at least a Year and a day (plus the amount of time that has passed since the start of the series, as we have yet to receive confirmation on any of their birthdays) before Ruby. However, since something as trivial as birthdays is unlikely to be brought up in the show, we'll just say that Yang and Ruby were born exactly two years apart.

So what could lead to the sisters having two different mothers? One possibility is that their father maintained a marriage with both mothers at the same time. This is unlikely, however, as it doesn't make sense to maintain the mystery about it, and its frankly terrible writing.

Another possibility is, as you stated, that the relationship between Yang's mother and father was abruptly ended in some way. This is more likely than the last, but if this were the case, Yang would have been born before the relationship ended, as the mother would not have left her father and then make him take care of Yang later. As stated earlier, we're assuming that Yang and Ruby are exactly two years apart, it may be a little more or a little less. Either way, this means that the timeframe between Yang's birth and Ruby's conception is only a year and three months. This is an incredibly short time for their father to get over separation with Yang's mother, meet Summer, and form a relationship with her. There is the potential for it to be shorter as well, given that we don't know when the separation occurred. Therefore, if we take this theory, the most logical prediction would be Yang's mother dying from childbirth, or deciding that she could not handle raising a child. Either way, due to Ruby's relationship with her mother, we know that Ruby spent a good deal of time with her. This would mean that she spent a good deal of time with Yang as well. However, we have not seen any indication of Yang's relationship with Summer Rose. It is possible that Summer did not hold the same love for Yang as she did for Ruby, due to Yang not being her child, but this theory involves Summer and Yang meeting when Yang is only a year old. It seems unlikely that Summer and Yang would have such a rocky relationship for Yang to be seemingly completely indifferent about her death. It is possible for Yang to have seen Ruby's distress over Summer's death, and decided to bury her own feelings and act happy for Ruby's sake, but this does not explain Summer's lack of acknowledgement of Yang in RLR2.

So both of the previous theories seem to have some flaws with them. Allow me to put forth this idea: Yang's mother was never married to her father. Taking evidence from Red Like Roses Part II, we know that Summer was a fighter of some kind. It is possible that Summer and Ruby's father were married before Yang was born. Summer could have been fighting in a war or on some extended mission, with Ruby's father being stuck at home without her. Their father could have had an affair with Yang's mother, which would explain her absense. Summer would make it home to discover that her husband had a child with another woman, and be furious, but they'd work it out and stay together. However, Summer would hold resentment toward Yang, while giving her full love to Ruby. This would explain why Yang is not mentioned in RLR2 by Summer, and why Yang doesn't show any signs of distress over her Summer's death.

If we look at this from the other side, with Summer having an affair with their father who was married to Yang's mother, this contains more holes than Swiss cheese, including Ruby and Summer's relationship, and Yang's mother's absense.

And now for the whole point, their names. Looking at theory 1, it would make the most sense for the two to have different names as they have different mothers despite the fact that they were in the same family. In theory 2, Yang's last name could be out of respect for her mother, or simply her father's name, while Ruby's name could be the request of Summer, or as you stated Ruby's decision, but it could also be Ruby's father's last name as well, assuming the first option for Yang. In theory 3, Yang's last name would most likely be the mother's, while Ruby's last name would be Summer's for obvious reasons. In theory 4, it would be the same as theory 3.

So yeah. The main point is we don't know why the names are different, and we simply have to wait for the story to get there.