No, the only way is to force the players to do that.
Example 2 starting positions, 1 for player. the first one is part only of Objective 1, the second is part only of objective 2. Everything else can be shared. obviously the 2 starting positions can't be taken by the opponent (pl1 can't take position 2 and pl2 can't take positions 1). The only thing...this is valid only for 1vs1 map, with the normal map type would be a problem with assassin games.
Have the 2 starting positions as non combat able territs (not able to be attacked or bombarded), linked to each of the objectives. So P1 can take objective one but as P1 cannot attack P2 start, they cannot gain the objective for P2. As for objective name, not sure you can have the same name as I have never seen that, would it not confuse the xml?