A geostationary orbit is a circular orbit in Earth's equatorial plane whose rotation period matches that of the Earth.
The "geo" in "geostationary" means Earth, so is there another term to designate similar orbits around other planets?
I'll go with Emily Lakdawalla who in her blog post about stationkeeping in Mars orbit wrote (emphasis mine),
What is a geostationary orbit like at Mars? I have to pause here for a brief discussion of semantics. The authors of this paper discuss "areostationary" for Mars orbits as opposed to "geostationary" for Earth, and Wikipedia uses the same convention, but I'm not a big fan of this sort of nomenclatural hair-splitting. You'd have to talk about "hermestationary" for Mercury, "cronostationary" for Saturn, "selenostationary" for the Moon, and so on. It gets tiresome. And while a very few people use "areology" to name the study of rocks on Mars and "selenology" to talk about rocks on the Moon, nearly everybody calls it all "geology" and a person who studies all that stuff a "planetary geologist." So I'm going to stick with calling it a "Martian geostationary orbit."
In addition to Martian geology and Martian and geography, people also write and talk about Martian terrain and Mars as a terrestrial planet. All of these terms, along with Martian geostationary orbit are incorrect from a pedantically correct point of view. The solution is easy: It's the overly erudite attempts at being pedantically correct that are incorrect.
Geostationary orbits are synchronous orbits, which are also circular and equatorial.
You could describe orbits around other planets in the same way, as circular, equatorial & synchronous orbits.
For Mars, the terms areostationary and areosynchronous are (sometimes) used. This follows the convention of how apsides are named, so it is likely that the convention used for apsides would be re-used for those orbits.
Note that this is all descriptive. We will know what terms catch on in the scientific and aeronautic community once there is the regular need to talk about such orbits and to distinguish them.
Some alternatives one might consider:
Perhaps "Clarke orbit"?
The definitions always talk about Earth but at least it's not in the term.
Consider the middling-future, when humans have put probes around other stars and other planets. We have run out of old Gods to mash into names like areostationary.
In this case, "geostationary" or "stationary" or one of the other generic naming conventions appearing in other Answers is appropriate.