"Name" here means the level of an intimacy of person with God or a level of growth of man in infinite divine Grace, the two being the same. Thus, there is and will be a hierarchy in the Kingdom of Heaven, as there is a hierarchy of angelic hosts. Thus, in earthly realm a man can be called "Andrew", which means "courage[ous]" in Greek, but in reality this man could be a coward; however if the same man through divine grace will really become courageous, then he will be really given the hidden name "Andrew" and it will be a real and new name for him, describing his inner character, which is symbolically expressed by "giving a white stone with an inscription of his name" which only he and the heart-knowing (Acts 1:24) God knows.
That this hidden name describing man's character or heart is known only by man himself and God, is clear: a really courageous man can be regarded as coward by by-standers if this man, for instance, does not respond to an insult, but uses the divinely obtained courage to oppose the rage that started to boil in him through this insult, defeats this rage and only then responds gently and calmly to the offender. This equanimity can be regarded as lack of courage by unspiritual bystanders. But the man himself knows and God knows, that he bears the invisible tablet with the new name of "Courage" in himself, and could of course have smashed the offender's teeth, but did not do so for love of God and His salvific commandments. (I do not speak about sorry cases of loathsome pusillanimous hypocrisy, when a coward "christens", so to say, the ugly baby of his cowardice by the holy name of "Forgiveness", which is spiritually worse than if that person had really beaten up the offender giving a free vent to his just rage).
Thus, this new heavenly name can be received and must be received also in our present earthly life, for we must grow in intimacy with Lord, overcome sins and get more and more full with the infinite grace of Lord, aiming at perfection (Matthew 5:48).