On private property, no permit is needed. A container in your driveway, on a vacant lot you own or inside a fenced construction site sits outside the city's rules entirely, and Rockwall publishes no container permit of any kind.
The street is where Rockwall differs from most Texas cities, and the difference runs against a street placement. We read the city's whole streets, sidewalks and public places chapter, and it does not contain an obstruction permit at all. Its sections cover the abutting owner's duty to keep the right of way clear of weeds and brush, driveways and culverts, the storage of vehicles, public art and the city cemeteries. Neither the word dumpster nor the word container appears anywhere in it.
The practical effect matters more than the detail. Because there is no permit limb to apply for, there is nothing the City can issue that would authorize a container in the roadway, so a driveway or a job-site placement is the only position the code plainly supports. If the only workable spot at your address is in the street, raise it with the City before you book rather than after delivery.
There is one nearby rule that catches people on shared sites. Rockwall makes it unlawful to put trash or garbage into a container on someone else's property without that person's permission, so a container on a multi-tenant lot needs the owner on side first.
Rockwall's own website would not load for us, so we are not quoting a city phone number here. Your account manager will track down the right department contact for your address before the truck is scheduled.