I was noticing that the two famous droids from Star Wars, C-3PO and R2-D2 have a four character alphanumeric name. Now, these are just two of so many droids out there, but I was wondering, in the Star Wars universe - do all droids have a four character alphanumeric name? If not, does the length or having an alphanumeric name as opposed to purely digits or characters have any significance?
We have at least one droid whose 4-letter title was just a fragment of a real long designation:
Cassian had killed K-2SO (whose true designation was far longer and far grander, rich with meaning and history that described his factory of origin, the date and time of his initialization, and more) and brought him back both smaller and larger than he had been. K-2SO did not mourn for his old self, but there were times he grew wistful over what he had been.
("Rogue One" official novelization by Alexander Freed, Chapter 19)
Pablo Hidalgo (Internet Content Provider for starwars.com) answered this conclusively in Q&A in Star Wars Insider #58 (Page 97)
He said that 4-letter robot names are just fragments of long serial numbers. And some droids don't even have a shorter 4-letter name for some, who instead get a real nickname (e.g. Corran Horn's Wistler).
Please note that the canonical status of Star Wars Insider information is questionable in new Disney canon, but Pablo Hidalgo is still pre-eminent canon expert at Lucasfilm Story Group, and as such the fact that a nearly identical fact was included in a canon novel probably means that the overall general rule also remain canonical.
The Force Awakens will feature a droid named BB-8.
Also, according to this answer, there was an R2 unit named R2-Z13.
As for the length of a name, I can find no information to suggest that it signifies anything special.
There are many counter-examples. One of the most plentiful droid types in the galaxy is the B1 battle droid. Their predecessors were the OOM-series battle droid. In an earlier question just a few hours ago I identified an RIC-920 general labor droid. Some droids, such as the droideka, don't appear to have any numbers in their name.
Droid names are usually derived in part from the droid series (e.g. R2 and 3PO) to help identify the function and capabilities of the droid (e.g. "B" in B1 is probably to indicate that it is a battle droid). The series name can have a variable number of characters (likely depending on how many related droid series there are). On the other hand, more unique droids like the droidekas do not need a series name for identification. Characters which are not part of the series sometimes identify a sub-series (e.g. the B2 super battle droid vs. the B1, and the E-3PO is from the 3PO line but is distinct from C-3PO droids). Longer droid names are probably used in order to avoid name conflicts with previous droid models.
Droid names appear to be assigned similarly to, say, real-world firearms (and probably for a similar reason). For example, M-series firearms often denote American firearms, numbers indicate different firearm models (e.g. M16 vs. M4), and other characters indicate different versions of a particular firearm model (e.g. M16A1 vs. M16A3). On the other hand, modern German firearms usually start with "G" (e.g. the G36, which has its own sub-variants like the G36C and G36K). Most Russian assault rifles start with AK, with the number usually denoting the year it entered service (e.g. AK-47 vs. AK-74), but not always (e.g. AN-94). You get the idea...