Will named be affected by changes to daylight savings rules in my location?

Usually no, as it is most common for machines to keep track of time using UTC and apply adjustments to display in local time according to OS-specific configuration rules.

For most OSes this change just means that you need to update the conversion rules from UTC to local time. On Unix and Unix-derived systems this normally involves updating a file in /etc (which sets the default timezone for the machine) and possibly a directory which has all the conversion rules for the world (e.g. /usr/share/zoneinfo). When updating the OS, do not forget to update any chroot areas as well if you are running BIND in a chrooted environment. See your OS's documentation for more details.

The local timezone conversion rules can also be done on an individual basis by setting the TZ environment variable appropriately. See your OS's documentation for more details.