What is the current theory and has there been a reliable answer?
The most celebrated theory that it derives from 秦 (Qin, as in the first dynasty, or the preceding state) I find a bit suspect. In contemporaneous times, it was pronounced something like [dzjin]. Are there examples of foreign transliterations that retained the voiced initial? Moreover, 汉 (Han) [xans] was certainly the more enduring dynasty of note from that period, and 楚 (Chu) [tshrjaʔ] the state before that. It is odd that the lineage would trace to 秦 and not to 汉 or 楚.
Of course, this isn't unprecedented. The Russosphere still knows China by the Khitans, whose state isn't even in the orthodox dynastic historiography †, but that is one data point in favor of a northwestern state being in good position to transmit its name to Eurasia. Still, what is the evidence that we can trace back China to 秦?
It is generally thought that Chīna, Sīna and Thīna are variants that ultimately derived from Qin, which was the westernmost state in China that eventually formed the Qin Dynasty. There are however other opinions on its etymology (See section on China above). Henry Yule thought that this term may have come to Europe through the Arabs, who made the China of the farther east into Sin, and perhaps sometimes into Thin.
There is Latin Sina and Ancient Greek Thina [th-], but it's not clear what these refer to.
The existence of the word Cīna in ancient Hindu texts was noted by the Sanskrit scholar Hermann Jacobi who pointed out its use in the Book 2 of Arthashastra with reference to silk and woven cloth produced by the country of Cīna.
There is Sanskrit Cīna (how is this pronounced?), which the continuation says may refer to some other geographic area like Tibet or Burma, from India's vantage point.
The English name for "China" itself is derived from Middle Persian (Chīnī چین). This modern word "China" was first used by Europeans starting with Portuguese explorers of the 16th century – it was first recorded in 1516 in the journal of the Portuguese explorer Duarte Barbosa. The journal was translated and published in England in 1555.
There is Middle Persian Chīnī. While it would make sense for Persian speakers to transmit the name of a western-most state, since they were the ones in direct contact, it is odd that Middle Persian has palatalized the initial and aspirated it. Does this correspond to something closer in Old Persian to which 秦 the state was contemporaneous?
Any other thoughts welcome.
† This is badly worded, see comments for clarification. The main point is to highlight the peripheral nature of the Khitan 辽 (Liao) state in analogy to the 秦 state.