Is it possible to attach extra text labels to components in Altium PCB?
This @Hneel's own answer but spelled out after I tested it for myself:

From the PCB library, edit your part to have a .Label in the silk layer placed where you want the text to be
In the schematic, add a parameter called Label to your part and set the value to whatever you want the label for that part to be on the PCB.
Once you update the PCB from the schematic, Altium will replace .Label on your part with the value of Label parameter set in the schematic

Tested using AD20.