How to search for a space in chat?

String patterns are just what you need. I recommend splitting the string after the signal character(s) (in your case, the ";;") into a command and argument.

local SignalCharacters = ";;"
local Message = ";;setHealth Username 100"

function HandleMessage(Message)
	if Message:sub(1, #SignalCharacters) ~= SignalCharacters then
		-- Return early if message isn't a command
		return
	end

	local CommandSubstring = Message:sub(#SignalCharacters + 1)

	local Command = nil
	local Arguments = {}

	for Match in CommandSubstring:gmatch("%w+") do
		-- If there's not a first match yet, it's the command!
		if  Command then
			table.insert(Arguments, Match)
		else
			-- If there's not a first match yet, it's the command!
			Command = Match
		end
	end

	if not Command then
		return
	end

	-- Continue here to check if it's a valid command, and has the valid number of arguments, et cetera.
end

HandleMessage(Message)