Korean given names feel much more personal as they are technically unique. As in: the parents get to be creative when naming their children.
Meanwhile, the surnames mean much less on personal terms. When your surname's called in the streets, you'll never think someone's looking for you.
So yeah, I feel it would be better for Min-jae's morale and motivation if his given name was used more frequently in Bayern.
Fun fact: 'Son' is a less common surname in Korea, accounting for 0.8% of the population. Meanwhile, 'Johnson', a relatively common surname in the US, accounts for 0.6% of the population.
Source: My Korean ass. Oh and I googled the last bit.
Could you elaborate further to a non-German?