What’s in a name? When developing the modified Ford Mustang that would eventually win the 1965 World Manufacturer’s Championship, Carroll Shelby named the car GT-350. The prefix made sense; it was the classification in which the car would race. Rumor has it that “350” was the distance in paces from the assembly building to his office. To which he is often quoted, "If it's a good car the name won't matter, if it's a bad car the name won't save it!"
In the category of semiconductor devices, neither the prefix nor the root part number generally makes any sense. If anything, the prefix has some meaning – although this has often been lost in the passage of time.
Let’s examine the prefixes of a few analog semiconductor manufacturers.
Fairchild Semiconductor was famous for the first IC, a flip-flop in what would become the micro-Logic family. At the time, integrated circuits were always called microcircuits and Fairchild abbreviated with the Greek Mu, µ. Hence, their logic family had the prefix µL. At the time, there were no linear ICs – that would have to wait for Bob Widlar in 1963. Fairchild always referred to their analog line as “linear” but the “L” had already been used. The references are unclear, but it’s safe to say they chose “A” for analog.
µL = Micro Logic
µA = Micro Analog
However, Fairchild used an order numbering scheme that did not use the “µ”. The format was “U” for microcircuits, two digits for the package type/number of leads, a microcircuit code for which “linear circuits” were always 7, the device number itself, the temperature grade, and finally one character reserved for special designation (standard devices were “X”). Hence, the µA709 in a 5-lead TO-99 package and -55°C to 125°C operating range had the number: U5B770931X. 
National Semiconductor likewise had different prefixes for different types of components. For analog, they used:
LM = Linear Monolithic
LF = Linear FET
LH = Linear Hybrid
Texas Instruments embedded the name for the different types of components within the root part number – the ubiquitous SN74XX###: 74 for commercial temperature logic (54 was military temp.), “XX” denoted the process technology and the rest of the number was the part function.
The prefix SN stands for “semiconductor network”.  The very first IC announced by T.I. was the SN502, a $450 flip-flop and they referred to the logic family as “solid circuit”.  “Semiconductor Network” was a TI name for the IC that seems to have replaced “solid circuits” and the SN prefix is still use today.
Maxim simply used “MAX” as the prefix, although second-source devices started with MX and another letter to indicate the company whose products they were second-sourcing.
Analog Devices used "AD" but eventually added additional letters to signify specific functions or product families.
Linear Technology did basically the same thing, LT for Linear Technology. However, Tom Redfern revealed that the investors were pushing for Linear Technology to offer CMOS analog circuits. That’s why Tom joined. The CMOS circuits got the prefix LTC to distinguish the process. It did not mean Linear Technology Corporation.
Several companies such as Precision Monolithics Inc. (PMI) and Burr-Brown used a more descriptive prefix. Operational Amplifiers had the prefix OP or OPA, references were REF, digital-to-analog converters were DAC, and so on. Today, Analog Devices carries on the PMI prefix in many devices, and T.I. carries on the Burr-Brown prefixes.
The IC prefix and numbering convention diverged significantly from the diode and transistor conventions that engineers were used to. In the U.S., the JEDEC convention was utilized. JEDEC was founded in 1958. The first semiconductor devices, such as the 1N23 silicon point contact diode, were still designated in the old RMA tube designation system, where the "1" stood for "No filament/heater" and the "N" stood for "crystal rectifier". The first RMA digit thus was re-allocated from "heater power" to "p-n junction count" to form the new EIA/JEDEC EIA-370 standard.  Another short-hand interpretation was that the first digit is the number of leads minus one. An ordinary bipolar transistor has three leads, so the first digit for it will be 2. The letter N is for semiconductors.
Despite the intention to make numbers logical or easily able to be deciphered, we remember the good parts. If it’s a good part, the number won’t matter. If it’s a bad part, the number won’t save it.
 Fairchild Semiconductor, Linear Integrated Circuits Application Handbook, 1967, written and edited by James N. Giles
 Andrew Wylie, http://homepages.nildram.co.uk/~wylie/ICs/monolith.htm
 JEDEC, Wikipedia.org