James Sirius....Albus Severus....Lily Luna....
I absolutely disagree. Did anyone think it was odd when George named his son after his brother, Fred? When Percy named his daughter for his mother, Molly? When Lupin and Tonks chose to honor her father when they named their son Teddy? Harry and Ginny, in choosing the names James and Lily, chose to honor Harry's parents. Sirius was Harry's godfather, and no one would be naming a child for him, so he chose to honor him in a middle name. I can understand why Harry would pair the names of James and Sirius, since the two were best friends. I think they wanted Luna to truly know that she did have friends who truly cared about her, so they honored her by using Luna for a middle name. Lily Luna sounds great together.
Albus and Severus would never have offspring and no siblings with children, so Harry and Ginny chose to honor them as well. I think the two names were paired because they were both Headmasters and they both helped significantly in winning the war. I'm no fan of Dumbledore's, but Harry was. And I don't often take Rowling to heart when she talks about the series, but in the case of Snape, she said on Twitter that
Snape didn't die for 'ideals'. He died in an attempt to expiate his own guilt. He could have broken cover at any time to save himself but he chose not to tell Voldemort that the latter was making a fatal error in targeting Harry. Snape's silence ensured Harry's victory.
she also said that
In honouring Snape, Harry hoped in his heart that he too would be forgiven. The deaths at the Battle of Hogwarts would haunt Harry forever.
Source
These ideas make complete sense to me.
Although, I do have to admit, Dobby Hedwig would have worked nicely as well!