Once you convert the timezone name into the corresponding UTC offset, you only need to add or subtract that offset value to convert back and forth between UTC and that local time.
I'm not aware of any standard library functions that convert timezone name into UTC offset; you probably need to write your own. For that matter, I'm not aware if there are even internationally recognized standard names for the timezones.
If you are only converting between UTC and the local time of your computer, then see if mktime, gmtime, and localtime (in time.h) can help you.
You need to decide how you want to handle Daylight Savings Time: as part of the timezone name (CDT vs CST) or as a separate argument.
By the way, be aware that some locations have non-integral offsets from UTC. For example, the UTC offset is -03:30 in some parts of Canada, +04:30 for Afghanistan, +05:30 for India, +05:45 for Nepal, etc.