Sekiro - Anayama The Peddler Questline Guide
You first run into Anayama in the Hirata Estate. As you move through the ravaged estate, you can run into him taking advantage of the chaos and searching for some new items to sell. As you progress through the game, you will find him again at Ashina Outskirts, at the bottom of the steps where you fight the red-eyed Chained Ogre.
Anayama The Peddler Questline
When you find him in the Ashina Outskirts, you can pay him 50 Sen for information about Hirata Estate, effectively starting his quest line. Paying him a further 100 Sen will get you the location of the Flame Vent Shinobi Tool in Hirata Estate. If you have already found the item, you will get two Oil pots instead.
Anayama will then tell you that he needs to know what the Ashina Samurai want, so he can find what it is they need and sell it to them. To find this out, you can eavesdrop on two enemies in Ashina Castle, near the Old Grave Sculptor Idol. This will allow you to find out that they need salt, and you can return to Anayama and tell him. The next time you rest at an Idol, his stock will increase.
At this point, Anayama will tell you he needs a strong worker to help him loot the battlefield. He needs somebody big and strong, and if you help him find such a person, he will be able to sell more useful items. At this point, you need to find Kotaro, The Crying Monk. To make Kotaro work for Anayma, follow the linked guide to get the Red and White Pinwheel, then give it to Kotaro.
Finally, after the attack on Ashina Castle that occurs late in the story, Anayama will move his little store just a small distance, as the original was destroyed. He will only sell one item, the Promissory Note. When you purchase this from him, it will result in the end of his quest, and also his death.
Now, one of the most important items you can buy from Anayama is the Phantom Kunai, an upgrade material for your Loaded Shuriken Tool. If you don't buy it from him before his death, it should become available through the box beside Hanbei the Undying at the Dilapidated Temple.
It is also important to note that you can kill Anayama when you first meet him in the Hirata Estate. If this happens, you will also need to wait for the Phantom Kunai to show up in the donation box.