At first, I only knew about 特朗普 for representing the US President's name, since it follows Xinhua's transliteration scheme. However, the World Journal uses 川普 exclusively, even in its articles written in simplified characters. That makes sense for World Journal, considering that 川普 sounds like a Taiwanese transcription to me, but Google gives almost as many results for 川普总统 as for 特朗普总统, making me wonder: which is more immediately recognizable to Chinese speakers?
Would using one or the other sound particularly regional, or politically biased?