You can copy the external functionality but not the internals. And a number can’t be copyrighted.
So you could produce the Dog80555®™ chip, with specified functions as described in your data sheet.
One may or may not be a drop-in replacement for the other, depending on application.
I’m not a lawyer, but I’ve spent some time working with IC chips.
The name is not the same. Each manufacturer has their own name and data sheet which is not necessarily exactly the same as the first one and one manufacturer will probably have more than one version. See for example 555 timer IC - Wikipedia
For a long time, National had a monopoly on their prefix naming convention:
LM = Linear Monolithic
LF = Linear FET
LH = Linear Hybrid
Other manufacturers could make pin-compatible devices, and give them the same number, but they wouldn’t have the same prefix (TI would use UA, Fairchild KA, Motorola MC, etc.) It’s only in the last decade or so that some manufacturers are using nearly identical part numbers. I’m not sure what has changed.
Note that when an IC manufacturer comes up with a commodity part, they are often compelled to license the design to other manufacturers, since big consumers want the ability to “second source” the parts.
Note that LM317 does not designate any device in particular, it is the generic name of families of devices which include even others with different names like LM117 and LM 217. You cannot order or buy an “LM317” without being asked more specific data. You need to specify manufacturer and specific device including case (TO3, TO220, DIL, etc.), temperature range, grade (military, automotive, life support critical, commercial, etc.), packaging (tape, reel, etc). All those things go into a much longer order code which most often is completely different between manufacturers. Generally the two first letters indicate manufacturer, just like with the 555 IC.
In any case, why would a manufacturer care that someone else is using the same or similar name. All the have to do is prefix a couple of letters for the manufacturer as is normally done and the full code is different. MC for Motorola, TI for Texas Instruments, etc. So you say “SE555 - Direct Replacement for LM555”.
Most designers are hesitant to use single-sourced products whenever they have a choice. Designing logic in the days of 7400-series TTL chips meant laying out the boards utilizing only chips you could buy from both a primary and a backup source.
Semiconductor companies (especially Motorola) would frequently share their data and explicitly license other companies to produce their chips, specifically because many engineers wouldn’t use them otherwise.
When I worked in that business in the 80s, it was common to see each part on a schematic listed with a primary and several secondary sources, and engineers would design to the least common denominator.
After making sure that the second source was truly independent - there were a number of cases where a second source was licensed and then either re-branded parts from the original, or the other way around.
There have also been cases where the “second source” agreement simply involved the second source buying finished wafers from the original company and doing the bonding / packaging themselves.
Since neither supplier is willing to tell you this, it often only gets discovered when the actual sole source has a problem and availability is constrained.
And things can get even funkier - the DCJ11 was completely built by Harris, but you could only buy it from DEC. And if you wanted one, you needed to talk to the product manager (Kathy I-forget-her-last-name) and justify why you wanted to buy them! Of course, given the number of errata on that beast, you probably didn’t want to design it into something anyway. Somewhere around here I have (what is presumably) a mockup of a DCJ11 with CIS (modules on the bottom as well as the top) encapsulated in a clear resin block. I assume it is actually a dud regular DCJ11 with fake CIS modules on the bottom.