The first time Sisko calls him "Julian"
I'm back on my spreadsheet bs (finally, it's so nice to be back!) and I've just got to Season Three and my Siskoshir heart cannot wait until I do the main analysis to talk about Sisko calling Julian "Julian"...
SO-
Right, so far Sisko has used Julian's name twice - once in Armageddon Game (2x13) when Julian is presumed dead, to tell Dax "Find out how I can contact Julian's family."; the other is in The Abandoned (3x06) when he introduces them both to the Jem'Hadar child as "I'm Benjamin, and that's Julian."
Usually, when talking to Julian (55/64 times in the 1st and 2nd series, to be exact), he calls him Doctor, and Past Tense (3x11, 3x12) is no exception. BUT, in 3x11 he calls Julian by his name for the first time and it's clearly not just random.
On the first day as they are talking, Sisko uses "Doctor" 4 times - but on the second, when Sisko wakes him up with food, he says, "Here you go, Julian." :3 :3 :3 I leave it to you whether that is the first time he uses Julian, whether they got closer the night before as they talked, or if it's been said off-screen many times; but I think it's significant that this canonical shift happens right here.
There are three more times Sisko calls Julian by a name in Past Tense:
Later that day when Julian asks to take a look at Webb's boy, Sisko simply says "Julian." to try and stop him (it doesn't)
That evening, when Bell has just got killed, and Julian is upset that he hadn't had a medkit to save him, Sisko changes back and says, "You did all you could, Doctor." :3
When Dax has arrived and they've all caught up with each other, Sisko says "Julian, I want you to help Dax find the men who took her comm. badge and then I want you both to get away from this place."
(And of course, that's the bit when Julian replies, "Sir, obviously Jadzia has got to leave... But you're still going to need help to keep those hostages alive, and if it's all the same to you, I'll stay." Which, 🥰🥰🥰, but also Julian responding with "Sir" to it is interesting idk 🤷♀️)
An addition:
Sisko does not use first names very often:
at this point he has never called Nerys or Miles by their first name (tbf neither have most of the crew)
of the 8 times he has called Dax "Jadzia", 6 were from episodes where he was differentiating between her and the Dax symbiont AND her life was in danger. By contrast, he has called her "Lieutenant" 19 times, and "Dax" 51!
he even calls Odo "Constable" about 60% of the time, rather than using his name, unlike most of the crew
So I think it's actually pretty significant that here he does choose, for whatever reason, to call Julian by his first name. And it has melted my heart just that little bit more for them :3 :3 :3