Why does Last Order state her name twice? I understand that the regular clones speak in third person from the answer here. But Last Order actually has emotions, so there is no reason to speak in third person or repeating her name over twice. What is the true reasoning behind Misaka wa Misaka wa ...?

Is there a canonical answer for this?
To understand why she speaks like this, we need to understand the grammatical rule for "wa" in Japanese. I'll admit that I do not understand Japanese fluently and I am a beginner, if anything, but let's take a look at what it can mean. For reference:

http://japanese.about.com/library/weekly/aa051301a.htm

The first one implies that the "wa" is a subject marker and she using herself as the subject. She has emotions unlike her sister clones and her having emotions mean that she can feel a variety of human characteristics. What I'm saying is that it is possible she repeats her name in this manner to draw attention to herself, to show that childish selfish characteristic. And we can see that she sometimes has no consideration about what other people feel, like how she (seemingly) unintentionally refers to Yomikawa as an old woman in one the bathroom/shower scene. Although this can be explained as her being playful, but I believe this still reflects her childish selfish nature, not that she's actually incapable of feeling empathy.

"Wa" can apparently be used as emphasis for the subject at hand, so this gives more credence  to my theory. From my reference:

"Beside being a topic marker, "wa" is used to show contrast or to emphasize the subject."

Although I can be wrong on this one. 

"Wa" as a contrast does not work well as it does not explain much. 

So it may be that she repeats herself in this manner to grab and draw attention to herself much like a child would. Aside from her being just a child, perhaps she does this to distinguish herself from the other clones.