"Attempt to index number with Name" - What's wrong?

You're just picking up a random number, not the value from the table. You'd need to use plrs[n]

So, the code you have would essentially do this:

local plrs = Players:GetChildren() -- consider changing to Players:GetPlayers()
local n = math.random(1, #plrs)
-- n = random number between 1 and the no. players
game.ReplicatedStorage.StringValues.Player1.Value = n.Name
local n2 = math.random(1, #plrs)
-- n2 = random number between 1 and the no. players
game.ReplicatedStorage.StringValues.Player2.Value = n2.Name

Therefore you're trying to say for example 3.Name, which of course doesn't make sense. If you want to get the actual player object, you need to index the table plrs using the nth value you got from before.

As so:

local plrs = Players:GetPlayers()
local n = math.random(1, #plrs)
game.ReplicatedStorage.StringValues.Player1.Value = plrs[n].Name
local n2 = math.random(1, #plrs)
game.ReplicatedStorage.StringValues.Player2.Value = plrs[n].Name

However my final solution is simple. First principle of programming: DRY

Don't

Repeat

Yourself

And using that rule, we can use a simple for loop to make this more elegant and easier to adjust should we want to add more players to StringValues.

local plrs = Players:GetChildren()
local numPlayers = 2

for i = 1, numPlayers do
    local n = math.random(1, #plrs)
    local val = game.ReplicatedStorage.StringValues:FindFirstChild(string.format("Player%d",n))
    val.Value = plrs[n].Name
end

I hope this helps and answers your question, if it did, please make sure to accept it :)