Just trying to establish where canon originally stands on this.
Giles and the Scoobs want to keep knowledge of Buffy being the Slayer a secret as much as possible. For the most part they succeed.
Now let's get into it though, because this continues into future seasons.
The Freshman written by Joss Whedon
Sunday doesn't appear to know at first Buffy is the Slayer, until she sees her dust one of her vamp crew.
He attacks. She uses his own momentum to keep him off balance and stakes him when he charges again. He disappears into dust. Behind Buffy, Sunday watches from a concrete dais.
Sunday: Slayer! (Buffy turns and sees her.) Wow, uhm, I heard you might be coming here. (The other vamps come out of hiding and surround Buffy.) This is, I mean, what a challenge! The slayer!
Sunday has been able to hunt at the college campus at will, because the slayer is in town, and in high-school. If that was about to change wouldn't a smart cookie like Sunday keep her eyes peeled for Buffy Summers. We know she can find her by name if she wants to, because later she does just that.
Sunday tells her crew Buffy won't last the night and sends her crew to the tunnels. Not to the dorm, to the tunnels. The tunnels are where they hunt. They can gather information there.
Buffy goes to town to her mother's house. When she returns to the dorm she finds this note in her empty room-
This is all just too much for me. I have decided to take off. Sorry I didn't have time to say goodbye but I need to be by myself. Good luck this year.
Buffy'
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The initiative don't know Buffy is the Slayer at first.
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From The Real Me by David Fury
DAWN VOICEOVER: If this town wasn't so lame everyone would completely know what she does.
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Demons don't appear to know where she lives, but they do know she hangs out at the Magic Shop. In the replacement by Jane Espenson Toth first looks for the Slayer there.
GILES: Oh!
TOTH: (raising his stick) The slayer is not here.
Other groups who do not seem to know to look for Buffy at her house when hunting her in Season 5 are the demon gang who's nest she burns down, and the Knights of Byzantium.
Later in Family by Joss Whedon the Lei-Ach also seek Buffy at the Magic Shop.
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In Family Glory discovers Buffy is a Slayer from the Lei-Ach demon.
GLORY: A slayer?? Oh god, please don't tell me I was fighting a vampire slayer! (Puts one hand to her forehead) How unbelievably common! If I had friends, and they heard about this
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In Flooded in Season 6 by Jane Espenson the M'Fashnik demon obviously doesn't know Buffy is the Slayer. He wants to kill the Slayer, but Warren has to give him her address so he'll know where to find her.
WARREN: (whispers) Here's the Slayer's name, address, and telephone number. You wanna kill her? Make it so.
The demon takes the paper with a low growl, leaves. Warren pats him on the back, turns around and sees the others watching him. Warren swaggers back over to them as they stare, impressed.
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Surely the 2 vampire teenagers in All the Way don't know Dawn is the Slayer's sister, cause if they do, they're the dumbest vampires on record.
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In Once More With Feeling Sweet has to be told Dawn is the Slayer's sister.
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In fact even Marti Noxon appears to know where canon stands on this issue when it suits her. In Villains by Marti Noxon, demons have been sitting in a bar watching television. There has been a news story covering a girl shot in her backyard. Addresses and or names are normally given out with such stories, but the writer who told us Buffy's name is so famous it has reached all four corners of the world now tells us the local demons don't know that the shot girl is the Slayer until Warren tells them.