Legal Question in Employment Law in California

I'm not sure what you mean by "register.". You can have the court from which the judgment issued prepare an abstract of judgment, and then you can record it with the recorder in the county where the judgment debtor owns property. You can also have the same court issue a writ of execution and deliver it (and copies) with appropriate instructions to the sheriff in which the judgment debtor owns a business, has a bank account or other assets.

The superior courts of each county have state-wide jurisdiction to enforce judgments. There is no reason to do anything in another county from the one where you have the judgment. If the judgment is from another state or country, it is another story.