For this specific application, it may be better to think in terms of a Lot Number for each batch instead of individual serial numbers. This will still let you trace back an item for where it was originally allocated, and greatly simplify your processing.
Under this plan, you create the STL file for the basic part and before each printing batch open the base file in even a simple tool like MS 3D Builder or TinkerCAD to emboss your number and the date, re-slice, and print.
I actually recommend a deboss here, where the text is recessed into the piece instead of extended outward. In this way it will be more difficult to file away without damaging the part, and again, even the basic modelling tools can quickly customize an STL file in this way.
If you really need individual serial numbers, design the part with a basic recessed rectangular cutout and print these in bulk. Then print individual plates the exact size (very slightly smaller) than the cutout with the serial number and date debossed, and superglue the plates down.
Finally, be aware there's a limit to how small the text can be, based on the size of the nozzle and the capabilities of the printer, and you may find it difficult to print very small text.