Not sure about hg and ss, but in g&s, they are Brock in Pewter, Misty in Cerulean, Lt. Surge in Vermilion, Erika in Celadon, Sabrina in Saffron, Janine in Fuchsia, Blaine in Cinnabar( but gym was relocated to Seafoam because gym was destroyed by volcano), and Blue(Gary) in Viridian.
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Go to the Kanto region and try to beat their 8 gym leaders.
go to serebii.com it tells how
defeat all the other gym leaders
To get all 16 badges in Pokémon Gold you need to first beat the 8 Gym Leaders of the Johto region and then defeat the Elite Four and the Champion of the Johto region in order to become its Champion and unlock the Kanto region and then in order to get the remaining 8 badges you will need to beat the 8 Gym Leaders of the Kanto region.
actually there isn't 9 gym leader there is only 8 like the other ones. Actually, the 9th gym leader in heartgold and soulsilver would be the first gym leader in Kanto after you beat the elite four the first time, you can face the kanto gym leaders in any order.