Good topic.
I like the idea of awarding a Playoffs MVP trophy. As has already been pointed out, the best player throughout the first 3 rounds of the playoffs might not make the Finals so their play goes unacknowledged.
On the other hand, the championship is ultimately decided in the NBA Finals. The first 3 rounds are easily forgotten during the Finals because the team that can win 4 games will be the NBA champions. The player who can lead his team to the ultimate prize will be considered the most valuable player of the championship winning team - even if he didn't have an impressive playoff before the finals.
I think Bob Petit is the only player to win the regular season MVP award in a season where his team did not make the playoffs. It would be strange to award a Playoffs MVP trophy to a player who did not lead his team to the Finals. I would suggest that two trophies be awarded, but that seems a little much. Ultimately, the Finals MVP is the player who has succeeded in taking his team to the title, so in the end he has been the most valuable player during the playoffs.
Thus, my vote goes to keeping the award for the most valuable player of the NBA Finals series.