You're essentially asking about the decipherment of cuneiform. There's always more to say about the topic, but I wrote about it in When did the modern understanding of the history of Bronze Age Mesopotamia develop?

Also see When and how were cuneiform languages (like Akkadian and Sumerian) first deciphered by modern scholars? by u/WedgeHead and If Sumerian is a language isolate, how was it deciphered? by u/farquier.

As for Kušim in particular, there is uncertainty as to whether this was a person or an administrative group. This is discussed in Archaic Bookkeeping: Early Writing and Techniques of Economic Administration in the Ancient Near East.

In this respect, a number of texts bear a particular sign combination, read KU and ŠIM, which together probably form the designation of a specific person, but which, on the other hand, may denote some sort of institution or economic unit. Indeed, since the archaic texts only mention individual characteristics, it is often extremely difficult to decide whether such sign combinations denote an individual, his office, or an entire institution.

Robert Englund, one of the authors of Archaic Bookkeeping, returned to the topic in an article published about 15 years later ("The Smell of the Cage" in Cuneiform Digital Library Journal Vol. 4).

To this discussion I would like to add some material concerning Late Uruk personal names that have often been cited in literature generated by the Berlin based project “Archaic Texts from Uruk,” but never gathered systematically, and that I have only ordered in a preliminary way. The major difficulty in isolating clear instances of personal names, where we must expect that the accounts and perhaps sections of the lexical lists were replete with such designations, is that the text formats do not explicitly identify what is what once you leave the realm of numerical notations, object designations and signs or sign combinations of thematic meaning derived from the lexical lists. Of course, we have been unable to identify, nor should we expect to find, any semantic glosses of personal names—aside from the simple number sign representing “one unit,” these were a millennium off. Frankly, one of the more dissatisfying discussions that I had with Peter Damerow and Hans Nissen in preparation of the Berlin Erlenmeyer exhibition catalogue was in fact having to admit that we could not state whether the sign combination “KU ŠIM,” central though it was to understanding the archival meaning of the core texts in this collection, referred to a human, to a profession, or to a household. We agreed to an individual “human” (brewery foreman), but only as an expedient convention.

There is little point in looking for the earliest named individual in Sumerian texts. Tablets from the Uruk period are notoriously difficult to date, and there are still hundreds of thousands of unedited texts. There have been quite a few publications of Uruk texts since the publication of Archaic Bookkeeping in 1993, such as Salvatore Monaco's Archaic Cuneiform Tablets From Private Collections (2016) and Englund and Nissen's Archaische Verwaltungstexte aus Uruk: Vorderasiatisches Museum (2005). In other words, the claim that Kušim is the earliest known individual is without any concrete evidence. There are other names and signatories on the Kušim tablets (e.g. the official Nisa), to say nothing of the other Uruk and Proto-Elamite tablets that may well predate the Kušim texts.