You can set a server time on Moodle and users can set their own timezones in their profiles.

And for some users/sites, the timezone setting may be forced.

In any case, its not always clearly obvious what the timezone for the time displayed is.

It would be helpful to show the times with timezones, especially on sites where users are spread across different timezones.

There can be a site-level setting to show timezones or not, so that it can be conveniently turned on or off depending on need.

There has been some discussion on this topic already on Moodle.org:

• Request to developers: Please display clock time always with its time zone
• Question about timezone