A further note to take of is this:
From the
Shibboleth of Fëanor
Quote:
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The Sindarizing of these names as Fingon and Turgon shows knowledge of the sound-changes distinguishing Sindarin from Telerin, but disregards meaning. If these names had actually been ancient Sindarin names they would at the time of the coming of the Exiles have taken the forms Fingon and Turgon, but they would not have had their Quenya meanings, if interpretable at all. Possibly they would have conveyed 'Hair-shout' and 'Master-shout' [see note 36]. But this did not matter much since old Sindarin names had by that time frequently become obscured by sound-changes and were taken as names and not analysed.
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This can be interpreted to mean that while Arothir is the correct
sindarized name of [Orodreth], that does not mean that it was the one that was used, because as said in the previous quote, some of the old Sindarin names had been obscured by sound-changes and were taken as name and not analysed.
Plus the fact posted by Aiwendil that Orodreth the Steward of Gondor had that name because of [Orodreth] the King of Nargothrond.