The kanji in Mana's name, 未那, can be read "Mina" or "Mana" depending on how you read the characters (on'yomi vs kun'yomi, or any combination of the two).
The meaning that makes sense to me is that her name is derived from 末那識 (manashiki), Manas-vijnana:
is the seventh of the eight consciousnesses as taught in Yogacara and Zen Buddhism, the higher consciousness or intuitive consciousness that on the one hand localizes experience through thinking and on the other hand universalizes experience through intuitive perception of the universal mind of alayavijnana. Manas-vijnana, also known as klista-manas-vijnana or simply manas, is not to be confused with manovijnana which is the sixth consciousness.
To put it simply, the name is self-referencing. The meaning of the name implies the ironic pun of the action (thinking). Much like an earnest person named "Ernest", which is an aptronym.
Edit: It has come to my attention that there's another bit of wordplay involved.
The 未 in Mana's name, 未那, refers to things that have yet to happen. The 末那識 uses a different kanji, 末, note that the top and bottom strokes are swapped around. While pronounced the same, their meanings differ significantly.
The latter kanji, 末, refers to the end of something, be it the edges or the end result.
The former is the same character used in the word for future, 未来, while the latter is the same kanji as in 期末, meaning the end of a term or semester.
So it would seem that Kokuto replaced the latter with the former in Mana's name. In other words, replacing a "conclusion" with a "beginning." When you think about it, the double-meaning in itself is pretty clever. Now I know how Shiki (式) felt.