By the wording, no. I'll break it down.

When you hack and slash, choose an ally.
-Pretty straight forward. You hack and slash, then pick a party member.

Their next attack against your target does +1d4 damage.
-The highlighted parts are the important ones. Next attack implies that it is one attack.
-Obviously, the your target part implies that it has to be the same creature that you're fighting.

Now, if you're asking if the paladin were to make repeated attacks against a target before the person with the boon makes one, you're either running your game wrong or your players are trying to game the system. I don't believe this was intended to be a build-up buff. In most games, buffs like these are not stacked. I would say that if there were two paladins and a fighter, that the fighter could be named by each paladin, giving him +2d4 when he attacks the same creature that both of them are attacking, but having two of the same classes in Dungeon World is another bag of worms. I think that this is really up to the GM to decide. If your players are trying to do something cool and unique, let them, but if this is them trying to break the rules to a point where they're going to use this tactic every fight, make them suffer for trying to do that. For instance, an easy one would be that on a miss, give him an extra d6 of damage while using this super-charged attack.