Is my touch script working properly?

That's because "Handle" is the argument of the function, meaning that whatever touches TryArea1 will be the one manipulated by the function (if you let it).

A function's parameter (whatever is in the parenthesis) can be name as whatever you want it to be.

function Example(argument)
end

function Example2(dfjkdslfjaksda)
end

function Example3(omgomgwowwhy)
end

But, of course, if you want something done to the argument, make sure capitalization and spelling are exact.

function Example(argument)
    print(argument*2)
end

function Example2(dfjkdslfjaksda)
    print(dfjkdslfjaksda)
end

function Example3(omgomgwowwhy)
    print(omgomgwowwhy+omgomgwowwhy+omgomgwowwhy)
end

-- TO USE THESE FUNCTIONS FOR A SPECIFIC PURPOSE --
-- You can place the argument you want in to the parameter (the things in between the parentheses)

function RelayTheExamples()
    Example("I like cookies.")
    Example2("What's 9 + 10?")
    Example3(7)
end
script.Parent.Touched:connect(RelayTheExamples) -- 'Touched' is one of the plethora of events Roblox provides

OUTPUT:

I like cookies.

What's 9 + 10?

21

If you want to only send a print of the handle, use an 'if' statement.

workspace.TryArea1.Touched:connect(function(Handle)
    if Handle.Name == "Handle" then
        print(Handle)
    else                -- 'else' and the next line are optional
        print("fail")
    end
end)

What the If Statement is Doing:

If the name of the handle is "Handle", then print "Handle"; otherwise, print "fail".

NOTE ON THE UPDATE

The argument can't be accessed outside of the function. "otherPart" will return an error because it is an unknown global variable.