How do I get the name of an Index in a Dictionary?

Well, for one Dictonary[1] in your case would happen to be nil, because the value at 1 is not defined.

However, to obtain a key based on the value (Do note it has to be the exact value, something similar won't count.), you can use an approach like the following:

local FindFirstKey=function(Table,Value)
    for Key,Val in pairs(Table) do
        if Val==Value then
            return Key
        end
    end --Returns nil by default.
end

Dictionary = {
    ['Index1'] = "Hello",
    ['Index2'] = "Goodbye",
    ['Index3'] = {PartObjectValue,PartObjectValue,PartObjectValue}
}

local Key=FindFirstKey("Hello")
print(Key) --> "Index1"
--HOWEVER this approach only works for exact values.

Key=FindFirstKey({PartObjectValue,PartObjectValue,PartObjectValue})
print(Key) --> nil

This occurs because you're making a new table, which technically isn't in the original!

However, this is worked around by actually passing the table that does exist in the dictionary

local RealTable=Dictionary["Index3"]
print(FindFirstKey(RealTable)) --> "Index3"

Then again, I doubt you have any actual use case for that.

TL;DR: A simple pairs loop should do the trick.

Your indexing it like it's an array. But, its a dictionary. When we think of dictionaries we need to think of key = value pairs. Meaning that a key returns a value. The best way to index a dictionary is this.

--Array Example--
Array = {1,2,3}
print(Array[1]) --> Output = 1 -- Since Lua Indexing Starts At 1. Unlike, Other Languages Such As Python.
--Dictionary Example--
Dictionary = {
    ['key1'] = 'value1'
    ['key2'] = 'value2'
    ['key3'] = 'value3'
}
print(Dictionary.key1) --> Output = value1 -- Since The Key Returns The Value
--How You Should Index Your Example--
--Unlike the example above, you have an array in your value. So, this is a special case, but since we know how to index an array and a dictionary, we can combine these techniques, to index this DictionaryArray!
  DictionaryArray = {
    ['key1'] = {1,2,3},
    ['key2'] = {4,5,6},
    ['key3'] = {7,8,9}
}
print(DictionaryArray.key1[1]) --> Output = 1

Also, eternal_silverfox's method works as well. But, should only be used if you don't know what key your looking for.

Hope This Helped!

More On Lua Here: https://scriptinghelpers.org/guides/lua-quick-start-guide