In season 1 episode 15 "Singularity" of Stargate SG-1, Frasier indicates the girl found on the planet has "traces of the stargate element in her". Sam replies with "Naquadah?".
When did they determine this as the element?
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Teal'c likely told them, soon after he arrived on Earth.
From the Stargate Wikia page on Naquadah:
The word "Naquadah" was first used in the Stargate SG-1 episode "Singularity", without explanation of how or when the mineral was named. Logically, Teal'c introduced the mineral's name to humanity after defecting to the Tau'ri. It was mentioned as a powerful additive for an explosive, but not named, in the original Stargate movie.
It makes sense that Teal'c would provide as much information about the Goa'uld including the primary materials used in weapons and buildings. He would definitely have been quizzed by SGC for useful information after defecting.
Stargate SG-1 continues the story from the 1994 Stargate film. While dialing the Stargate for the first time, Catherine Langford tells Daniel Jackson that they know that it was built with a mineral not found on Earth.
Catherine Langford: My father found [the Stargate]. 1928. Made out of a mineral unlike any found on Earth.
After Daniel Jackson and the rest of the team goes through to the planet (named "Abydos" in the series), they find a mining village. While there, one of the soldiers scans the metal they are mining and later tells them that it's the same material the Stargate is made out of.
Sgt. Brown: I took some readings of what they're mining back there. It's the same material as the Stargate.
When Daniel Jackson discovers the history of Ra, he learns that not only the Stargate, but the rest of Ra's technology (ships, staff weapons, etc.) is made from the same mineral.
Daniel Jackson: This mineral is clearly the building block of all his technology. With this, he can sustain eternal life.
However, the team never learned the name of the element. When Sgt. Brown scanned it in the mining camp, the team couldn't communicate with the locals, so they couldn't ask them. By the time they could communicate, there were much more pressing issues, and then they went home shortly after defeating Ra (with Daniel Jackson staying behind on Abydos).
There are three possibilities for when they learned the name "naquadah":
Given that the first two possibilities involve someone that Stargate Command trusts, and they happen chronologically earlier, I think that it is far more likely that they learned the name "naquadah" from Daniel Jackson than from Teal'c.
Note also that in the pilot episode, "Children of the Gods", Daniel Jackson gives a lot of names to things that had not been named in the feature film, like the name of the planet being "Abydos". I find it impossible to believe that he would not have known the name "naquadah" at that point. Also, I hardly think that Stargate Command would be asking Teal'c "what is the name of the element used in the Stargate" when they had more pressing questions to ask him.
Also note that in the episode "Singularity" (which had the first on-screen mention of the word "naquadah"), they were talking about it because they were dealing with a bomb laced with the stuff. If for some reason Daniel or Teal'c still hadn't told them the name, I'm sure that they would have asked Daniel about it given that Ra, another Goa'uld, also laced a bomb with naquadah.