If I'm not mistaken, the earliest official historical record of Dai Viet only appeared in the late 13th century in the form of 大越史记 which is itself mostly lost. Terms like 李朝 and Ly Thanh Tong comes from 14th and 15th century history works like 大越史记全书. If so, titles like Lý Thái Tổ might have been given by later posterity, not by contemporaries and his immediate posterior title was simply 太祖 or 神武皇帝(both of which are also given to Chinggis Khan by Qubilai). I wonder whether there are primary sources from Song times with terms like 李朝.Yeah, I understand your point when you bring up Xixia, Liao and then Jin. The two former existed in a world, say, post-Tang, and became a regional power that potentially challenged the authority of Song state. Dai Viet was also a newly created independent kingdom during this time. But the, how to say, the convention of naming the state is quite different, and you can see that from the title of any Xixia, Liao or Jin emperors. Li Yuanhao was also called Xia Jingzong, or Xixia Jingzong according to some books I read. When the state of Xixia was annihilated by the Mongols, no kings were named as such, no state remained as such.
Now compare to the Vietnamese rulers. The Ly dynasty ruled their supposed "kingdom", or perhaps a confederation of different tribes, or a kingdom in which the power of the court still remained decentralized, how did they call themselves? Ly Thanh Tong (Li Shengzong), Ly Nhan Tong (Li Renzong). What is the name of the dynasty? Ly dynasty! But what is the name of the state? Dai Viet. Tran dynasty, Dai Viet; Le dynasty, Dai Viet. Sure, there was a period of times when the name of the state was changed, and this was clearly recorded in their histories, but it was later removed and reverted to the old name. Ho Quy Ly changed the name of the state in to Dai Ngu (大虞), which wasn't endeared by the modern Vietnamese since the "Ngu" also means stupid. It is this tradition that we call up on.
Furthermore, Dai Viet was in fact not the continuous state name since the founder of the Le dynasty, for the original title of the state since its breakoff from the Tang was 大瞿越 or Daqu Yue and the state name only changed to Dai Viet in 1054, and the founder of the Le dynasty was mentioned by Mengxi Bitan to be a person from the Min (Fujian) area "桓死，安南大乱，久无酋长。其后国人共立闽人李公蕴为主。" We also have the state of 闽越 in Fujian during the five dynasties, and I see Quyue and Minyue to be of the same type of state and a source from that period would shed more light.
I'm also not arguing for exact identicalness between Dai Viet and states like Xixia, which isn't true even among different "Chinese states"， and Dai Viet's southern location certainly puts it at a different model to those northern dynasties, but I've used earlier cases of dynasties during the 16 kingdoms period to show similar trends. The point is that nationalists today tends to group history based on boundaries of modern nation states, and they might well be drawing lines that are far more clear than it should be.
Did they express the same sense of continuity as shown in the case of Vietnamese dynasties? While the name of what now we call "China" was changed so many times, the same is not true for the Viets. The name "Dai Viet" or "Dai Co Viet" was first used in the X century and continued to do so up untl the XIX century, with different dynasties ruling it, even at times divided the country into different parts.
In this discussion, it seems that you limit your timeframe to the Song period, is that correct?
We have very little record from the 16 kingdoms, and all of these dynasties which I mentioned ended because they were conquered, had they lasted, they might have used the same state title for centuries. The title Liang and Yan did last for close to a century, and it switched dynasties and was also divided into several regimes all of which were called Liang (Western Liang, Northern Liang， etc) and Yan (Former Yan, Later Yan, Northern Yan).Clearly, an interpretation can be drawn from this, that they do not confound the name of a ruling dynasty with the name of the state. Dynasties could change but their state remain almost the same in name. The name Dai Viet must has some significance in it so that they still preserved it up until the Nguyen dynasty, right?
The Viet State lasted because it was able to repulse powers from the north repeatedly, from the Song, the Yuan and Ming, by which time a separate identity was firmly rooted for centuries. But if we are limiting our time frame to the Song, then the later periods aren't really relevant for comparison and that's where the question lies; did Dai Viet during the first 2-3 centuries of its existence really had that strong a sense of separate history.