Does informing someone of one’s intention to sponsor an orphan constitute showing off (riya') that voids the reward, knowing that one suffers from obsessive-compulsive disorder and does not intend to seek thanks or reputation?

Your words about sponsoring an orphan are not blameworthy ostentation, because merely expressing the intention to do good and resolving to do so is not blameworthy, unless it involves seeking people's praise or commendation. The Prophet, peace and blessings be upon him, did this when he said: "By Allah, I shall certainly raid Quraysh." As for blameworthy ostentation, it is observing people in one's actions, desiring benefit or praise from them, or safety from harm or blame. You should turn away from obsessive thoughts and occupy yourself with what is beneficial.