local matchNouns = {"<<", ">>"}
local matchOther = {"%f[<]<%f[^<]", "%f[>]>%f[^>]"}
 
local str = "<Hello> <<world>>, <my> <<name>> <is> <<John>>"
 
local function printOtherMatches(str)
    -- Get opening and closing brackets
    local open, close = unpack(matchOther)
 
    -- Concatenate opening and closing brackets with
    -- pattern for finding all characters in between them
    for other in str:gmatch(open .. ".-" .. close) do
        print(other)
    end
end
 
printOtherMatches(str)

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