Very good question!
The original nomenclature was developed by Philips in 1932.
The first letter (S) in fact does not mean Sodium, but a Single arc tube. Before this became popular there was a type having a double-folded arc tube, denoted by letter D.
The second letter (O) denotes an oxide-coated cathode. Originally there were directly heated electrodes, and these types were denoted by letter A.
So up to the mid 1930s sodium lamps were available as the types
DA,
DO and
SO. I don't think there was ever a type SA.
In 1955 Osram-GEC invented the Integral lamps having a sealed outer jacket. They denoted that by adding a letter I, creating the
SOI family.
In 1959 BTH-Mazda invented the
Linear lamps. At first it was just called an SO Linear, but a few years later they broke the above system by calling it an SLI lamp with the L meaning Linear. It seems the marketing people at the time did not understand the system used previously. It was later recognised that they should have in fact called their new lamp the LOI. But by then it was too late and the name SLI already stuck. It was also generally felt by then that S = Sodium and any new lamp should begin with S in its name. The company published some naming charts of their own in which they re-allocated the letter S to mean "Sodium", O to mean "One Cap" and the letter L to mean "Linear".
In 1963 Philips invented the improved Integral lamps having an infra-red reflective coating on the outer envelope. These new types did stick to the original naming structure and were called
SOX, in which X = eXtra efficient. Of course, that also fitted the naming structure that had in the mean time become popular in Britain, so GEC's IR-coated lamps of 1964 were also called
SOX.
In 1966 AEI-Mazda (the successor of BTH-Mazda) applied the same infrared reflective coating to its linear
SLI lamps but did not change the type letters to reflect that improvement. Once again that company diverted from the established practices - they should really have been called either SLX or LOX.
In 1965 Osram-GEC was first to introduce high pressure sodium lamps in Europe, but it did not assign any name to them. The following year AEI-Mazda also introduced its HPS types and denoted those as
SON, and as Max indicates the N simply meant New. Philips in Holland also adopted the same name.
Finally in 1974, Thorn (the successor of Mazda) introduced a linear high pressure lamp. You might think they would have called it the SLN, but once again they broke established practices and called it
SON-TD, in which the TD means Tubular Double-Ended. To add even more confusion, Osram-GEC then followed suit and launched its own linear high pressure lamp, and called that
SON-L. Then Osram-GmbH added its own linear variant and gave that the
-TS suffix, but I have no idea why they chose S.
As a result the naming of sodium lamps has become totally chaotic and there are a lot of misunderstandings about what the letters mean. The actual meaning also appears to have changed over time, and many books and manufacturers documents give conflicting descriptions of what the letters refer to.