Hi,
No, there is no such feature because the test log as a whole does not exist until the test execution is over (but the approach mentioned by Tanya will certainly work).
However, you may implement a handler for the OnLogError event (see help for more details on this and other mentioned TestComplete objects), get the name of the currently running test item (not a test code procedure name, but test item name), craft some message string and display it on the screen using the Indicator object.
Also, despite the full log is not available during test run, its .ErrorsCount, .WarningsCount, etc. properties contain actual values. So the simpler solution is also possible:
-- Create a Temporary Project Variable with initial value of 0 (zero);
-- Implement a handler for the OnTestStop event;
-- Within this handler, get the number of errors posted to the log;
-- Find the difference between the current number of errors and the value of the temporary project variable;
-- If the difference is not zero, this will mean that the given number of errors was posted to the log within the given test;
-- You can output obtained information using the mentioned Indicator object.
Does this help?