How do I index an abbreviated name?

You can take a substring of a string with the string.sub function. If you have string A equal to "Player1" and string B equal to "pla", you can take a substring of string A with the length of string B. These two strings can then be lowered with the string.lower function and compared.

local stringA = "Player1"
local stringB = "pla"
local abbreviatedA = stringA:sub(1, #stringB)
print(abbreviatedA:lower() == stringB:lower())

This functionality is quite simple to implement into your program:

local Players = game:GetService("Players")

local findPlayerKeywords = {
	all = function()
		local players = {}
		for _, player in next, Players:GetPlayers() do
			table.insert(players, player)
		end
		return players
	end,
}

local function getPlayersWithMatchingName(str)
	str = str:lower()	--	the findPlayer function has already lowered the passed string but not doing so here is considered a bad practice as we cannot assume all other functions to do it for us
	local matches = {}
	for _, player in next, Players:GetPlayers() do
		local abbreviatedName = player.Name:sub(1, #str)
		if abbreviatedName:lower() == str then
			table.insert(matches, player)
		end
	end
	return matches
end

local function findPlayer(str, allowMultipleMatches)
	str = str:lower()
	if findPlayerKeywords[str] then
		return findPlayerKeywords[str]()
	else
		local players = getPlayersWithMatchingName(str)
		if allowMultipleMatches or #players <= 1 then
			return players
		else
			return {}	--	alternatively nil can be returned, just keep in mind all the functions calling "findPlayer" have to take that possible outcome into account
		end
	end
end

Your code and actual question did have two contradicting statements. Your code hints that you do want to get a table of players as the output, yet your text states you either want nothing or possibly a player object. Thus I added the allowMultipleMatches option.