The bank matters, but the bigger thing is whether your bank profile, ARC, and carrier registration all match character for character. In Korea, a decent branch can still leave you with app verification failures if one system has your middle name spaced differently. If you open an account, I would test transfer limits, app login, and 본인인증 on the spot before leaving the branch.

One practical thing that helped me was doing 본인인증 tests before leaving the branch, not later at home. Ask them to check the exact English name spacing on the bank profile against your ARC and telecom record, because that mismatch is what quietly breaks Toss, bank apps, and card verification in Korea. It feels picky, but fixing it on the first visit is much easier than opening tickets afterward.