Counterbore has no effect on cards on the battlefield that have the same name as the targeted spell.
Counterbore
If the spell’s controller isn’t the same as its owner (due to Commandeer, for example), it won’t be exiled. The spell is countered and put into its owner’s graveyard. Then the spell’s controller’s graveyard, hand, and library are searched.
If the targeted spell can’t be countered (it’s Vexing Shusher, for example), that spell will remain on the stack. Counterbore will continue to resolve. You still get to search for and exile all other cards with that name.
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