Firstly I would like to make it very clear once again that Katerina Peristeri is doing an amazing job, and that her whole team are clearly very talented.
What I present is just my opinion based on their incredible work, and I am sure that when she presents her ideas they are more likely to be correct!
If my guess is Hephaestion based on historical evidence, logic and her work ... I am sure that she has given her candidate much more thought, but has been conservative in announcing it. So if she later announces Hephaestion, please give her credit for thinking of it first! If she announces someone else, I am sure she has very good evidence for him.
Also to clarify the swan found in the tomb.
I am aware that a self-published 'scholar' has been making wild guesses that Olympias is buried at Amphipolis, because he choses to ignore the many inscriptions saying she was buried at Pydna.
I prefer to ignore those kinds of wild and deliberate distortions of history.
I am aware of a story about a scorpion and a swan linked to Hephaestion. Please note that this is a modern children's story inserted into the movie Alexander, and Hollywood movies are not really considered historical sources!
There are many real myths involving swans, for example Zeus turning into a swan to seduce Leda; and since the Argeads claimed descent from the kings of Sparta, that story is more likely.
But my interpretation lies in the well known story that Phaeton was turned into a swan.
Phaeton is an interesting figure, and although Ovid wrote a different version of the myth, in this period he was linked to mourning. In fact the Belevi tomb, probably built by Lysimachus for his son, had figures of the Heliades his sisters standing between the columns as mourners for him (the statues vanished long ago, but the inscription identifying them survives). I interpret the women on the Mourning Women Sarcophagus as copying the women between the columns on the Mausoleum of Halicarnassus, and possibly also representing the Hecatomnid relatives of Mausolus as Heliades mourning him - in addition Helios seems to have been in the chariot that crowned the Mausoleum.
Therefore there are good arguments to be made for the daughters of Helios mourning their brother Phaeton, and Phaeton being represented by the swan he turned into.
Greek myths are better for historical interpretations than the semi-insane ramblings in Hollywood films.