My wife's name is Konpaku Youmu (魂魄妖夢). Her family name Konpaku comes first and means "soul". Her given name Youmu literally means something along the lines of " demon dream", "bewitching dream" or "wicked dream".
The official romanization has been consistent so far, mainly because it's a Japanese name, but I don't think ZUN treats romanization as something permanent; he's really inconsistent with foreign-sounding names.
The name appears to be completely made up and is obviously a reference to Reimu's name. It has the exact same number of kanji and morae like so:
博麗霊夢（はくれい れいむ）
魂魄妖夢（こんぱく ようむ）
I think this alone is already unique within the Touhou series and just like with Reimu's name, everything is Sino-Japanese. The meaning of the given name is also very similar: Reimu literally means "spirit dream". The reason for this similarity is most likely that Youmu originally was meant to be a rival character.
The kanji of Youmu's given name 妖夢 also appears in the title of the game she first appears in 東方妖々夢～Perfect Cherry Blossom as well as in the title screen theme 妖々夢～Snow or Cherry Petal and her stage theme 妖々夢～Ancient Temple. 々 is just a kanji repetition symbol, so 妖々夢＝妖妖夢. Reduplication of this kind is very common in Chinese, but I don't know what kind of connotation it has in Classical Chinese.
According to the afterword of the demo version of the game, 妖々(youyou) is a reference to a line in The Pillow Book by Sei Shounagon, a famous work of Middle Japanese literature from around the year 1000. The line in question is:
「春はあけぼの。やうやう白くなりゆく山際、少し明かりて、紫だちたる雲の細くたなびきたる。」
or
"In spring it is the dawn that is most beautiful. As the light creeps over the hills, their outlines ared dyed a faint red and wisps of purplish cloud trails over them."
So, 妖々(youyou) comes from native Middle Japanese やうやう(yauyau), which meant "gradually", cf. Modern Japanese 漸う(youyou) "gradually" and 漸(yaya) "somewhat".
However, 妖(you) was read as "eu" during Middle Japanese times, so the kanji usage only makes sense from a modern perspective.
Anyway, because of this Youmu's name gains a second meaning of "gradual dream".
Youmu's family name 魂魄(Konpaku) means "soul" in Japanese but as a Taoist concept ("hun and po" in Chinese):
魂(kon) is the spiritual soul that goes to Heaven upon death.
魄(haku) is the animal soul and goes back to Earth after death.
Normally, both types of soul reside within the body, but in Youmu's case part of her sould is her phantom half that's following her around. Most likely, the phantom half is her kon and the haku keeps her body alive.
However, that doesn't mean that there's just one kon and one haku. A popular Taoist concept that is referenced in two of Youmu's spellcards is 三魂七魄, according to which humans have three kon and seven haku. This confirms that 魂魄 is not just used as word for soul but the Taoist concept specifically.
In Touhou, the Konpaku family seems to be some kind of clan, but the only other known member is Youmu's predecessor Youki. Both share the first kanji 妖(you) in their given names, so I imagine that's a common theme within the Konpaku clan.
Something else that's of note: ZUN consistently writes 妖 as 幺夭 instead of 女夭 in his handwriting including in Youmu's name. I've never seen anyone else write it like that and it doesn't seem to be a common short form. Furthermore, the 幺 radical is very rare, so I doubt it's just a mistake.
This is supported by the fact, that he frequently uses a lot of kanji and words containing this radical such as 幽霊("ghost") or 幻("illusion"). As you can see, it often appears in kanji associated with the supernatural, particularly apparitions. The radical doesn't exist on its own in modern Japanese anymore, but ZUN notably used it to write 幺樂団(Yougakudan) and cryptically described as the ancestor of 幻樂団(Gengakudan). In this instance, he intentionally singled out this particular radical, uses it three times each and relates it to 幻("illusion").
I guess Youmu means "gradual, illusory, demonic dream"?
