"DocallisecDaemon" will do what now?

It definitely sounds like malware. Unfortunately, Apple's built-in malware protection leaves a lot to be desired. Yes, it does detect and disable the malware. But it doesn't remove the script that continually tries to load the malware. You'll need to remove that script. Apple stores these scripts in a hidden directory that isn't searchable.

The script is probably in one of the following locations:

/Library/LaunchDaemons

/Library/LaunchAgents

~/Library/LaunchAgents

In most cases, malware never tries to masquerade as anything else. Please try to read the files names in those directories. If any word in those file names sounds like anything that you recognize, then don't touch it. But if there is one that says something like "Docallisec", some other nonsense, gibberish word or a long string of numbers (with no associated trademark like "Adobe" - malware developers usually do respect trademarks funny enough), delete the file.

Good luck!