Saving a table of names via DataStore?

How do you go about saving the names of items in your Backpack to a table?

Well, you had no go at it at all yourself so I won't explain it at all. It will require changing to fit your needs...

ds = game:GetService("DataStoreService"):GetDataStore("Tools")
ds:SetAsync(game.Players.Player1.userId,game.Players.Player1.Backpack:GetChildren())

To retrieve the data store:

ds = game:GetService("DataStoreService"):GetDataStore("Tools")
tools = ds:GetAsync(game.Players.Player1.userId)

Iterate

local names = {};
for k,v in next, Player.Backpack:GetChildren() do
	names[k] = v.Name;
end;
DS:SetAsync(Key, names)

Assumes DS and Player are predefined as the DataStore and Player respectively.
Also assumes that Key is predefined.