I have read that the modern tendency is to translate a modern person's personal name into Latin but not his surname. So John Doe would be translated as Ioannes Doe. This seems sensible at face value, for people to understand who you are talking about, but it seems very complicated when you actually generalize this for every person mentioned and then try to talk about said persons interacting. So if Ioannes Doe decided to hit Ioannes Smith, how could we possibly make sense of who hits who? Smith Doe pulsat doesn't make any sense. You could contour that by always using their first name, so Ioannem Smith Ioannes Doe pulsat reveals that it is Smith who is getting beaten. You can even simplify this by only naming one of them, so Ioannem Smith Doe pulsat, which by context has Doe be the perpetrator. But are there any other strategies used by good Latinists to deal with the proliferation of indeclinables? Are there any authoritative sources that deal with this issue and any prescribed standards?
As cmw says, the most common solution was to simply…ignore the problem. In many cases, the ambiguity isn't particularly bad; there's a default of putting the subject before the object, and the context will often make it clear who's doing the action to whom. That's how it's done all through the Vulgate for example.
But some authors found other ways. The easiest is just to force the names into some Latin declension; now they're no longer indeclinable. Another is to put them in apposition to something which declines; in Classical usage, for example, names of alphabet letters are indeclinable, but you can talk about littera A versus litteram A. While Smith and Doe are indeclinable, Joannes is not.
For names, instead of apposition, you can use a demonstrative like hic or ille—or you can stick an article onto it. Even though Classical Latin doesn't have articles, some later authors back-ported the Romance article li for this purpose, or borrowed the article from Greek. This answer gives some fun examples:
... ne fortè ... per technas Imperium à se τῷ Aly destinatum præriperent.
…lest perhaps…through their artifices, they would snatch away the Empire destined by him for Ali.
In the end, though, simply ignoring the ambiguity (and relying on context or word order to disambiguate it) was the most common solution by far. This is also what Romance ended up doing when sound changes eroded the distinctions between the cases: sacrificing the free word order and relying entirely on the syntax for clarity.
You may not like it, but word order is necessary, and in fact is what was done with the Vulgate:
Abraham genuit Isaac Isaac autem genuit Iacob Iacob autem genuit Iudam et fratres eius
There's no way someone will read this and think "Isaac begat Abraham".
For most of the antiquity, it wasn't an issue, so Neo-Latinists have largely fallen in line with that precedent.
That said, context is key. In what non-textbook, real-world example would Smith Doe pulsat not make sense from context? Anything unclear could be made clear in the same way ambiguities in actual Latin could be clarified (hic/ille, putting one into passive, etc.).
There is a long tradition of translating personal names into Latin or Greek, especially in the Renaissance. One of my favourites is the German humanist Osiander, né Hosemann (“trouser man”, half done into Greek and half left in German). So John Smith could become Ioannes Faber. And John Doe could become Ioannes Cerva, or why not Cervus. Both parts are then declinable.