The history of the usage of the tern 'Internet' is somewhat murky; one of the first uses of the term was in 1974: in RFC 675 (Request for Comments) which was wrote by three individuals:
The title of RFC 675 is "Internet Transmission Control Program": this RFC document outlined an early host-to-host technical architecture. The Internet Transmission Control Program would later be split into two protocols: TCP and IP. TCP/IP are still the core protocols used by the Internet. TCP stands for the Transmission Control Protocol (TCP) and IP stands for the Internet Protocol (IP). Therefore, the word "Internet" was still retained in the name of one of the protocols, and due to IP being the core protocol, it is not surprising that this word would be used to describe the overall global system. While the three individuals who wrote RFC 675 are generally credited with coining the term "Internet", who the first person was to use the term is up to debate, it could be any of the individuals who are acknowledged as helping in the development of the "Internet Transmission Control Program" in RFC 675: R.Tomlinson, D.Belsnes, J.Burchfiel, M.Galland, R.Kahn, D.Lloyd, W.Plummer, J.Postel, R.Metcalfe, A.McKenzie, H.Zimmerman, G.LeLann, or M.Elie. Those familiar with the history of the Internet will instantly recognise the name V.Cerf: Vinton Gray Cerf is often referred to as a "founding father" of the Internet: due to him being the co-inventor of TCP/IP.
However, at that stage - the 1970s to 1980s - the term Internet was simple used as an adjective; aka, a word which was used to describe the inter-networking of transmission programs etc. Only by the 1990s was the term Internet used as a noun; aka, a word which denoted a thing: the network of computers which used the TCP/IP technology to communicate with one another. The term 'Internet' did have some competition in the 1980s; the term 'Information Superhighway' was another popular term used to describe the project of transitioning the backbone of IP networks from the U.S. federal government to autonomous commercial networks. The term Information Superhighway was used by U.S. politician and presidential candidate Al Gore. Al Gore is credited with providing crucial political support for the Internet's development in the 1980's and 1990's: as a Senator and Vice-President of the United States. However, by the year 1992, the term Information Superhighway was out of vogue, and the organisation formed to oversee the development of the Internet was named the Internet Society (ISOC). The term 'the cloud' has tentatively been used to describe some aspects of the Internet - as of 2010-2012 - but it does not describe the overall system, and, as the majority of organisations who design the technical architecture and decide policy of the Internet have the word "Internet" in their title, it is unlikely that any other term will be used to used to describe the global system of computer networks who use TCP/IP.