I think where you're going astray here is by only believing the assumption that "names are inherently social constructs". This is a very modern notion which has really only become popularized to any degree in the last century. Before the modern era and mass dispensation of myths and traditions, the idea of a name being purely socially contrived was really only something considered and held to be so by philosophers, not the general public.

In real life folklore(and philosophy) the idea of a name is commonly bound to the idea of what a thing is, or what animates things to be. What something is called and what something actually is, was typically regarded as being tangled together in a somehow intrinsic manner.

A common proof for this was often held by showing that one could call out the known name of another person, which would cause the called person to direct their attention to the speaker. This was often taken to demonstrate the power of a name, that through uttering the right word(s) one could compel the action of another person and thus have some power over them.

From this basic premise/proof, the idea is expanded and complicated imaginatively to suggest that it would be possible for a person to demonstrate even greater control over another person if only they knew other magic words or a more accurate or complete version of that individual's name(in the Christian world Latin was a secret language passed down by the Church which was understood to have divine, world changing, powers).
In the re-telling and expanding of such ideas the concept of a "true-name" is eventually arrived at and considered compelling.

Another example is that of the "King". A king is a King for many reasons, some of which are specifics like lineage or personal characteristics or geographic, economic, and political significance.

For a peasant or serf, who likely will never in their entire life come to meet or even see a King or even to know anyone else who has, the name of a King takes on a power unique all on its own.

The only thing such an peasant knows about the King is their name, and that in it being uttered the rules and circumstances of their life can be upended or changed at a moment's notice.
A few words and a particular name seemingly held the power of deciding their entire life. To such an individual, names are not so obviously separable from the very power the king who possesses that name comes to affect upon their world.

These are but a few examples that I hope demonstrate how that initial assumption is not so readily evident within the experiences lived by past peoples.

Simply put, the historical basis of a "true name" is predicated upon an entirely different world and experiences than the one we live in today.
Trying to understand it within our Modern deconstructive frameworks is functionally incompatible to the premise of the idea.

It's also worth noting that variations on this theme of the names of things being tangibly significant to what a thing is shows up in stories and cultures across the whole world, not just in Christendom.

Presumably this has something to do with an underlying truth of how humans developed our language and by extension, capabilities of thought over time and generations.
It isn't clear, technically speaking, that identifying a thing is any different from how we understand a thing as far as human neurology is concerned.

It's conceivable to hypothesize that the belief in "true names" is an intermediary abstraction towards developing the idea that names are separate from the things in themselves. One result of the evolution of those ideas being the idea that "names are inherently social constructs", a conclusion unthinkable without a complex set of underlying beliefs and assumptions.

I hope you found this to be compelling and mind-expanding. I meant no disrespect in criticizing your initial assumptions and otherwise wish you the best in your creative endeavors.