Absolutely yes, formatting takes place at the presentation level. Up to this point, you keep the data in all internal formats most suitable - for dates, which can be either DATETIME or the equivalent, or as a binary representation; which is best for sorting, storing, etc.
You don’t turn it into anything that actually looks like a date until it is displayed (or otherwise displayed in a human-readable form), at which point you convert it and apply any regional or custom formatting attributes.
These attributes are essentially your “format string” and you store them in a database (if centralized) or, possibly, a local configuration file on the user's PC. Personally, I tend to maintain standard or standard default rules in the database, and then add overrides for a specific user or region at the display point.
source share