There are already named items in game. You can sometimes find them at weaponsmiths. Guess there might be armor pieces too.
But the idea of gathering old relic pieces is a neat one. A little bit of indiana jones ruin exploration would be great. Like having it a secoundary or sub “quest” finding leads in taverns or even as loot from other camps. Could be done as an additional menu screen with limited collumns for limited random generated items like 3-5. And the leads would go in corresponding item collumn so you can always check it. Maybe map pieces like heroes of m’n’m did it or just clue texts. Small papper pieces which when mouseovered would tell the hints in the tooltip.
I belive it would be a great addition while wandering around the world fighting the “great evil”. This has a potential of filling up different places and ways with additional optional content. You could embed some real cool mystic stories in these hunts, and even follow them up with more special events or faction quests. The clues could be even quest rewards or choise of reward instead of plain money. There already are some nice story elements with the mistycal deliveries, relics and other interesting beginnings. This could be the logival next step.
Since this is quite similar to getting item as a reward instead or with money, that could be a thing too. We are in the midieval timeline afterall, barter and trade is a core element of this age, not only pure gold. I’d take a 2h sword as a reward many times over gold since in my games those seem to be hard to get. Just as some nice pieces of armor. Maybe even make events where you get to help a lone knight of perhaps a noble house to fight off attackers and if he lives you get reward in money and increased renown while failing to save him still gives you some of his knighty gear but the said faction would be angry with you.