There are some industry standards, and a lot of de-facto standards, and more ad-hoc imitation.
Back in the day, JEDEC registered parts could be produced by anyone, and sold as that part number so long as they met the spec sheet. (And many other provisions, I'm sure; I've certainly not read any official standards, or agreements, that might've been signed between such parties.) The thing you're buying is actually the spec, not, what's inside, how the part is made; this flexibility allowed multiple sources for standard components, which benefited the major customers at the time: growth of the semiconductor industry is closely tied with the military-industrial complex. (Which is more-or-less to say: they're one of the tentacles of exactly that complex.)
This is the origin of 2Nxxxx series parts, for example; the "2N" is actually JEDEC nomenclature, "2" being one less than the number of pins or electrodes (so, a tri-ode), "N" being a semiconductor device (hence 1N for diodes, 3N for certain MOSFETs, some optocouplers with 4N and 6N, and so on). This dates all the way back to vacuum tube days in fact (for example, I have a 2C53, a high-voltage triode; "C" must be hard vacuum type... although, 2E21 is a pentode, surely it should be 4-something? maybe there was a change of convention in there, dunno), so the early days of semiconductors were already accommodated by existing schema.
There are other basic-device nomenclatures in use around the world, too; or have been. 2SAxxxx (A, B, C, D, J, K) in Japan, and BCxxx (and other letters) in Britain/Europe (another schema dating back to vacuum tube days: EC91 is a 6V-heater (E) triode (C), for example), for two prominent cases.
As time went on, more and more advanced and proprietary devices were developed, and second sources were still stipulated; this forced negotiation of licensing terms between competitors, which explains, for example, how AMD obtained Intel's 8086-family designs.
JEDEC is -- I don't want to say less important, let alone unimportant, these days, but, outside of the industry at least, you don't hear much about them in regards to specific parts, and that's probably more to the effect that, the circumstances present in those earlier days, simply aren't around anymore, and standard parts have drifted away from industry-standard families towards proprietary ones.
Thus, we get de facto standards, like TIP31s made by everyone (literally, TI (Texas Instruments), 'P'lastic transistor, type 31); D44H11 is old GE nomenclature (later Harris, or maybe the discretes went separate ways, not sure offhand); MJE350 is old Motorola (I think, 'M'otorola, 'J'unction transistor, 'E' series plastic package, type 350); IRF540 (International RectiFier); etc. etc.
As for IC naming conventions, generally it's a few-letter prefix; µA for Fairchild, MC for Motorola (probably "C" for integrated Circuit), TL for TI Linear (I think??; also SN for digital, for some reason), LM and DM for National (linear/digital), etc. Many manufacturers second-sourced similar numbers with new prefixes, like how we have µA741, LM741; CD4013, MC14013; etc.
Probably, these days, there are few restrictions or limitations on who can make a part, or sell something as a given part number. You always have to be careful choosing substitutes: 3Peak makes a "LM2903A" for example, which looks to be a largely compatible imitation, but is most definitely a CMOS part, entirely unrelated to the original bipolar type. It doesn't even have to be a second source; the first-party can pull such tricks on you too. I recall a particular TI part offering a new CMOS version in the main-line datasheet, which could make for some awkward realizations when one is depending on typical bipolar behaviors.
Even just "ordinary" updates, revisions, die stepping, can cause issues; several STM32s, I think, have gained notoriety for having done this.
In summary: while there are some common parts, sometimes it's entirely coincidence (there's "2N3055" and "MTP3055", although maybe with ballpark-similar voltage and current ratings, but one is an NPN BJT and the other an N-ch MOSFET), sometimes it's imitation (2N2222A (TO-18 metal can) is a boutique part these days, but PN2222A (plastic TO-92) and MMBT2222 (SOT-23; Motorola lettering convention I think) are widely available), and you always need to check the datasheet to be sure.
Another example: µA/LM/etc. 723 regulator/controller ICs, a staple way back in the day; 2nd sources quickly dropped the original's buried zener voltage reference for a bandgap reference of comparable performance -- but noticeably poorer noise level.