Unless you are displaying a time with location information, I would just display it consistently in the local time zone.
Example 1: Check-ins
This is an example of where you WOULD want to show it in the specific timezone.
If you are displaying check-ins on a map. You would want to show the times in the relevant timezone. However, if you are a trying to establish a timeline around the viewer, you would provide either local times or the relative time.
–– CHECK-IN ––––––––––––––––––––––––––––––– 1 day ago ––
Location: New York, NY
Time: 8:15am (EST) on Tuesday
–– CHECK-IN –––––––––––––––––––––––––– 32 minutes ago ––
Location: San Francisco, CA
Time: 9:28am (PST) Today
–– UPCOMING EVENT –––––––––––––––––––––––– in 2 hours ––
Location: Dallas, TX
Time: 2:00pm (CDT) Today
Example 2: User Comments
This is an example of where you WOULD NOT want to show different timezones:
–– Comment by Joe ––––––––––––––––––
"This is great!"
–– Comment by David ––––––––––––––––
Using a consistent timezone for display values in this case is important for maintaining a clear timeline.
Naming Conventions fall under the Interaction Design (IxD) vertical. There are some good principles here that might help offer some insight.
Chris Dixon just shared some thoughts about display timezones recently as well.