It seems that integrated circuits of the 1970s tended to have 4-digit part numbers.
Not really. Anything from letters to numbers and 3 to 7 characters have been used. even with numbers like 7400, the chips name wasn't just the number, but a letter number combination, like SN7400.
Other than often assumed is SN not a prefix used to indicate TI, but the 'family' TI puts that chip into. 'Family' in quotes as it's not really a technological differentiation but rather organisational - exactly to avoid collisions if different divisions use the same number. In addition some of the prefixes are historical. Examples for prefixes used by TI are:
- CA - Analogue, inherited from RCA
- CD - Digital, inherited from RCA
- SN - 'regular' digital
- RSN - Radiation hardened digital
- SNJ - Mil Spec Digital
- TL - Linear
- TMS - Data Processing (computer)
There're might be more - we in digital electronics are simply way too used to 'SN', not seeing the rest.
Other companies made up similar distinction (Like Altera with EP/EPC/EPF), while on the other end small newcommers wanted to fit in and simply added their company mark in front, like CY for Cypress or MAX for Maxim. Important is, that all of these letters are integral part of the 'name', not just ignorable prefixes.
In addition people often add a manufacturers abbreviation to the name when needed, like TI-SN7400.
It looks like there was a global namespace of 4-digit numbers that all the companies used.
No, there wasn't. Every manufacturer used it's own system. Well, except there was an attempt to standardize names on functionality in Europe. It did make inroad for diodes and some analogue IC, but never cought on for digital/TTL.
Indeed it was common for a particular chip to be manufactured by multiple companies
Sure, if one wants to sell a compatible chip, he named it alike to pave the way for customers to find and buy his chips. Although, it did need a learning curve from marketing. Especially visible with early RAM (*1) and ROM chips, were functional identical chips had different names, leading to long lists of equivalent models.
Heck, even companies that licenced other companies designs re-'named' them. A good example would be AMD's AM9511 FPU of 1979(?), licenced and marketed by Intel as C8231.
This changed a bit when chip names, especially the numeric part, became household names if not brands (but really only a bit).
But I haven't seen any mention of a registry of numbers used, or any other central way of avoiding collisions.
Corse there was none.
How did they avoid collisions?
They simply didn't.
Was there even any such thing as a comprehensive catalogue of chips listed by number, that you could look up to make sure a candidate number wasn't already in use?
Well, there were huge IC databooks, sold for unimaginary high prices by third party publisher - 1000 USD for a comprehensive list wasn't out of the ordinary (and we're talking 1980s USD). But their use wasn't about avoiding collisions, but helping engineers finding the chips they need, or equivalent chips from other manufacturers - like when looking for a replacement or lower prices.
It was as well the high time of chip brokers, firms specialized in keeping an overview, consulting and often arranging a deal/sales.
*1 - For example chips compatible (or licenced) with the well known Mostek MK4116 16 KiBit RAM were available as (peeked from an old paper under my desk mat):
- AM9016 from AMD
- F16K from Fairchild
- MB8116/MB8216 from Fujitsu
- HM4716 from Hitachi
- 2117 from Intel
- M58759 from Mitsubishi
- MM5290 from National
- uPD416 from NEC
- MSM3716 from OKI
- LH6116 from Sharp
- N2690 from Signetics
Not to mention that Mostek as well sold them as MKB4116 in military grade and MKI in industrial grade :)