This is a question for which we do not necessarily have a good answer. Hong Taiji never specifically explained his motives for renaming the state of Latter Jin to the Qing Empire, and historians have been somewhat divided over the exact etymology of the name Qing. This argument over etymology actually serves as a reasonable jumping-off point for discussing questions over the Qing foundation more generally. To paraphrase from a previous answer:

1. The Chinese character qing 清, meaning 'pure', contains the water radical (氵); whereas the character ming 明, meaning 'bright', contains the characters for the sun (日) and the moon (月), and thus has associations with fire. The water-associated Qing would thus extinguish the fire-associated Ming.

2. The Mongolian transliteration of da qing 大清 is daiiching, which might have been a pun on the Mongolian word daiichin, 'warrior', and so another target of this change may have been the eastern Mongols whom the Qing were courting at the time.

3. Some Japanese scholarship from the turn of the millennium has suggested that early Manchu documents sometimes use the phrase amba cin gurun interchangeably with daicing gurun, suggesting that there could originally have been an intended near-homophone in Manchu that later fell out of use. Cin can be defined 'chief, principal, main' or 'straight, straightforward', so amba cin possibly meant something like 'The Great Primary State' or 'The Great Steady State' or something along those lines, as something rooted in essentially Manchurian/Northeastern precedents.

Now, a reasonable line of argument is that all three could be true at once: Hong Taiji hit on a name for his state that appealed to three distinct constituencies. And this is something we need to consider next: the multiple axes of Qing expansion. We tend to think of the Qing in the mid-seventeenth century as being predominantly preoccupied with the conquest of China, but this isn't necessarily the whole picture. By the end of the 1620s the Jin state had largely secured its base area in Manchuria and driven out any notable remaining Ming bridgeheads, and its major military efforts were now mainly focussed to the west towards the Mongolic steppe, and to the north up into what would ultimately become the Russian Far East. The most substantial Qing success would come with the surrender of Ejei Khan of the Chakhars, son of the recently-deceased Lighdan Khan, in 1635. Up until that point, the Great Yuan still technically existed, with the imperial seal passed down ultimately to the leaders of the Chakhar tribe; Ejei's surrender meant these seals now fell into the hands of Hong Taiji, and it has been suggested that it was in fact this particular prestige coup that led Hong Taiji to re-found the Jin as the Great Qing. As with the etymological issue, this raises more questions than it answers about Qing motivations. On the one hand, yes the Yuan was sort of 'canonically' part of the succession of Chinese states, and so the claim on those seals theoretically allowed the Manchus to also claim inheritance to the Mongolian claim over China. But equally, the dissolution of the Northern Yuan and the implicit claim of the Aisin Gioro to the mantle of Great Khan substantially increased the Qing's prestige claims in the steppe as well. So we cannot use this to really give a good accounting of Qing motives.

As Nicola di Cosmo notes in this rather substantial seminar talk, there is somewhat of a question as to whether the Qing conquest of China was at all premeditated, or rather an opportunistic response to the collapse of the Ming by a state whose ambitions had hitherto been more regional in character. We do, for instance, have Qing texts from the period where that end goal is at the very least implied and to some extent overtly stated: for instance, Nurgaci in 1622 is supposed to have delivered a speech to his troops stating that Beijing, Nanjing, and Kaifeng ought to be regarded as historically Jurchen as much as Han Chinese; Hong Taiji used the Chinese phrase da shi 大事 ('great enterprise') as early as 1631 to describe his intentions to Ming officers whom he was courting the defection of. But declarations of idealised ambitions are not exactly the same as declarations of practical intent. For instance, Nurgaci boasted that his armies would cross the Shanhaiguan by 1624, but such plans never even materialised, and in any case such a move could just as easily be a large-scale raid as an attempt at conquest. How to interpret all this thus is a bit up in the air. At one extreme you might have Frederic Wakeman's position, where the entire raison d'etre of the Aisin Gioro clan beginning with Nurgaci was the conquest of Ming-ruled China; at the other is Pamela Crossley's argument that this narrative is essentially false and largely the product of Qianlong-era teleological histories portraying the formation of the Qing Empire as preordained by heaven, while actual Jurchen-Manchu policy in the period was much more contingent and reactive.

What makes this especially hard is that state-building is something that can be pursued on its own merits without necessarily being directed at a specific external entity. Yes, the Manchus made substantial strides towards improving the quality and usage of gunpowder weapons, but just because they were getting better at siegecraft doesn't mean they were necessarily planning on taking over China as opposed, say, to Korea. Yes, they adopted a civil government structure modelled after the Six Boards used in China, but that doesn't necessarily mean they were planning on then extending that over China, as it could just be that the Chinese civil service was a tried and tested model that was easy enough to replicate. Indeed, as I stressed earlier, there were also Qing ambitions in Mongolia (indeed, most of what is now Inner Mongolia was under Qing direct rule or suzerainty by 1644) that were no less served by their military and administrative expansion.

We also ought to account for the formation of the Banners and indeed the Manchus here, as this is also a point of ambiguity. Firstly, the Manchus: in 1635, Hong Taiji had also proscribed the use of the word 'Jurchen' to denote the tribes he now designated as 'Manchu', which excluded certain tribes such as some of the northerly 'Yeren' tribes, disambiguated some liminal cases such as the Yehe Nara, and also included certain tribes that did not themselves identify as Manchu such as the Sibe. This designation, which can be seen as a deliberate break from the earlier Jurchens (see here for more), marked the beginning of the creation of a Manchu group identity tied specifically to what would become the Qing, and a discontinuity from the Jurchen Jin. This doesn't directly bear on the idea of a conquest of China of course, but it would be remiss not to account for the formation of the core of the conquest elite in the context of these mid-1630s developments. More broadly, the formation of the Banners is complicated because while yes, Han Chinese constituted a substantial (indeed, for some time a majority) component after the establishment of the Hanjun Banners in 1631, there was also a Mongol component for one, and for another in the long run the 'Martial Han' (Hanjun) of the Banners were considered somewhat ethnically distinct from 'civilian' Han Chinese in China Proper. Indeed, the Manchu terminology for the Hanjun Banners sidelines the notion of their being ethnically Han, using the term ujen cooha gūsa ('heavy troops banners') rather than the term for the Han, nikan, while 'Mongol Banner' (monggo gūsa) was still used for the Mongol Banners.

But, despite all the doubt I have cast above, it does seem reasonable to argue that some sense of a meaningful ambition to conquer China had coalesced by the early 1630s. Mark Elliott cites two pronouncements by Hong Taiji, one in 1632 and another in 1634, in which he expresses substantial concern over the prospect of an erosion of Jurchen cultural values after a conquest of China. Such concerns, expressed at such length, would not be reasonable on the part of someone without some genuine intent to see them through. One can ask when exactly Hong Taiji finally started moving things off the drawing board into actual policy, but by the latest I would say the period 1641-4, which saw the Qing reduce many of the last Ming strongholds outside the Shanhai Pass and launch major raids across the Great Wall, even before the revolt of Li Zicheng overthrew the Ming from within. That is not to say that the conquest itself was not perhaps opportunistic in terms of its timing: the Qing could not have predicted that the Ming state would be toppled domestically, after all. Moreover, as Peter Perdue has argued, the Manchu-led state was actually starting to run out of portable wealth that could be effectively distributed to keep the elites of its various constituents in line by 1644, and the collapse of the Ming proved to be a bit of a lucky break. But it seems reasonable enough to suggest that there was a distinctly Ming-oriented character to Qing state-building efforts under Hong Taiji, even if there may not have been a specifically planned timeframe for conquest.