Most common newspaper suffixes in the English-speaking world appear to have an obvious link to their function: News, Journal, Herald, and the like. Is the suffix "Times" simply another of these where the "news" meaning has fallen out of use or is something else going on here?
The 1700's saw the emergence of the newspaper and with it was eventually daily local news delivered.
The word "Times" itself started to appear in 1788 when The Daily Universal Register switched it's name on January 1st to "The Times."
So why do various newspapers have the name Times at the end? It boils down to the company lending its name to other papers including The Strait Times (1845) and The New York Times (1851) as some examples. Those newspapers adopted a similar format and writing style as The Times.
Sources: New Times, Good times by Thomson, Robert British Journalism Review, ISSN 0956-4748, 06/2005, Volume 16, Issue 2.
Nevins, A. (1959). American journalism and its historical treatment. Journalism & Mass Communication Quarterly, 36(4)
Edit: Sorry, had more to say but I wanted to answer your main question first.
For the other names like "Gazette" or "Herald", it was a generally accepted practice as a method of persuading readers. This first started in the late early 1600's with names like "The Intelligencer" and "Mercury."
Source: Bourne, H. R. F. (1887). English newspapers: chapters in the history of journalism (Vol. 1). Chatto & Windus. This book goes in to depth about who created them and about the names.