Delta 3914 launch vehicle lifts an RCA Satcom Domestic Communications Satellite at Cape Canaveral, Florida.  NASA intended Delta to be a general purpose vehicle used for communication, meteorological and scientific satellites as well as lunar probes during '60 and '61". (photo source: RCA Astro Electronics/Maxwell W. Hunter Foundation archive)

In his capacity of Chief Engineer of Space Systems at Douglas Aircraft Company, Max Hunter was responsible for the engineering for all Douglas space efforts, which included Delta.   The original Delta rockets used a modified version of the PGM-17 Thor, the first ballistic missile deployed by the United States Air Force, as their first stage.

The Delta design emphasized reliability rather than performance by replacing components including a radio ground guidance system mounted to the second stage rather than the Thor itself. NASA let the original Delta contract to the Douglas Aircraft Company in April 1959 for 12 vehicles of this design.

The Thor-Delta launched a number of significant payloads, including the first communications satellite, Echo 1A; the first British satellite, Ariel 1; and the first active direct-relay communications satellite, Telstar 1. All 12 launches occurred from Cape Canaveral Air Force Station Launch Complex 17. The launch of Telstar 1 used pad B, while all other launches were from pad A. All launches were successful except the maiden flight, which failed to place Echo 1 into orbit due a problem with the second stage.

The plan was to replace Delta with other rocket designs as they became available. From this point onward, the launch vehicle family was split into civilian variants flown from Cape Canaveral which bore the Delta name and military variants flown from Vandenberg Air Force Base which used the more war like Thor name.

How did the name “Delta” originate?
Thor had been designed in the mid-1950s to reach Moscow from bases in Britain or similar allied nations, and the first wholly successful Thor launch had occurred in September 1957. Subsequent satellite and space probe flights soon followed, using a Thor first stage with several different upper stages. The fourth upper stage used on the Thor was the Thor "Delta," delta being the fourth letter of the Greek alphabet.

Eventually the entire Thor-Delta launch vehicle came to be called simply, "Delta." The Delta name stems from its position as the fourth, or D version, of the Thor based rocket combination. The vehicle has been known both as Thor-Delta and simply Delta.

“Fifty years, dozens of upgrades, and more than 300 successes later, the Delta expendable launch vehicle remains the 'magnificent little workhorse' of space.The satellites and space probes it has launched have revolutionized several industries and expanded the boundaries of science, and Delta II has set a high standard for launch vehicle reliability — its record currently stands at 93 consecutive successes.”
Kevin Forsyth                       http://kevinforsyth.net/

A large family of space launch vehicles—the Thor and Delta rockets—were derived from the Thor design. The Delta II is still in active service as of 2014 and with the retirement of Atlas and Titan in the mid-2000s is the last surviving "heritage" launch vehicle in the US fleet, being derived from a Cold War-era missile system.

Delta II will soon be retired. Delta rockets are currently manufactured and launched by the United Launch Alliance.