I haven't voted as there isn't one that I particularly feel does the job.
As the best of a weak selection - Software Health - though I think that it can still be misunderstood, as with the others what software does it refer as many would think it only relates to avast!
RejZoR's suggestion 'Vulnerability Scan' is nearer to the mark as to what it actually does by ensuring your installed software is up to date and not 'vulnerable.' But I'm not sure about the use of the word scan, as there may be implications of avast just scanning the installed software in the same way as regular avast scans.
Perhaps 'Software Vulnerability Check,' but then that may be one word too many, perhaps 'Vulnerability Check.'