Database
[{"_id":{"$oid":"5ec4b8c87176dd2d544fd0ad"},"relationships":[{"rel_name":"HAS_TAG","rel_destination":"TAG"},{"rel_name":"HAS_CORE_TAG","rel_destination":"TAG"}]},{"_id":{"$oid":"5ec4b9377176dd2d544fd0ae"},"relationships":[{"rel_name":"HAS_TAG","rel_destination":"TAG"}]}]
Query
db.collection.aggregate([{$match:{"relationships.rel_name":"HAS_CORE_TAG"}},{$addFields:{relationships:{$map:{input:"$relationships",as:"r",in:{"rel_name":{$cond:[{$eq:["$$r.rel_name","HAS_CORE_TAG"]},"HAS_NEW_TAG","$$r.rel_name"]},"rel_destination":"$$r.rel_destination"}}}}}])