Here are some thoughts as they occur to me.

First, the Global Volcanism Program (GVP), which is the reference database in this matter, lists only one Holocene (i.e., considered active) volcano in Syria: Harrat Ash Shaam, to which Es Safa actually belongs. (There are also a few Pleistocene volcanoes in the country.) So I wonder what is this second one that the CIA mentions... As it is close to Turkey, it could be Karasu Rift, which extends into Syria.

Also note that these volcanic systems are extensive basaltic lava field, rather than a proper volcano, as in "single conical mountain with a summit crater", which makes their identification harder. They can have a large number of subfeatures (cones, craters and lava flows) that may or may not have been named individually. That could explain why the Syrian part of the Karasu Rift did not receive its own name, although some of its features might be known by a name by locals (if any, in such desert areas).

Second, it would not be the first unnamed volcano! If you scroll the GVP Holocene volcano list down to the letter U, you will see a dozen entries with the name... "Unnamed". Most of them are submarine volcanoes, which have probably been identified quite recently, but not all. (The International Hydrographic Organization is in charge of naming such discoveries, but it might take some time. A bit like the International Astronomical Union is in charge of naming planetary features. As an aside, there are still a lot of extraterrestrial volcanoes unnamed!)

Even a volcano with a name can be misleading. For instance, you might think that Bezymianny, in Kamchatka, has a proper name, until you realize that it literally means "unnamed" in Russian!

Here are some thoughts as they occur to me.

First, the Global Volcanism Program (GVP), which is the reference database in this matter, lists only one Holocene (i.e., considered active) volcano in Syria: Harrat Ash Shaam, to which Es Safa actually belongs. (There are also a few Pleistocene volcanoes in the country.) So I wonder what is this second one that the CIA mentions... As it is close to Turkey, it could be Karasu Rift, which extends into Syria.

Also note that these volcanic systems are extensive basaltic lava fields, rather than a proper volcano, as in "single conical mountain with a summit crater", which makes their identification harder. They can have a large number of subfeatures (cones, craters and lava flows) that may or may not have been named individually. That could explain why the Syrian part of the Karasu Rift did not receive its own name, although some of its features might be known by a name by locals (if any, in such desert areas).

As an example, take the Pinacate volcanic field, in Mexico. According to GVP, it comprises "more than 500 basaltic cinder cones and lava flows" (see image below). In Gutmann 2007, there is a "Pinacate volcanic field place-names" map (figure 5, that I cannot reproduce here), which has barely two dozens names. Only the most prominent features are named (Cerro Colorado, Crater Elegante...) while all the smaller cones remain anonymous.

Landsat 8 OLI image showing the Pinacate volcanic field in 2017. From NASA Earth Observatory.

Second, it would not be the first unnamed volcano! If you scroll the GVP Holocene volcano list down to the letter U, you will see a dozen entries with the name... "Unnamed". Most of them are submarine volcanoes, which have probably been identified quite recently, but not all. (The International Hydrographic Organization is in charge of naming such discoveries, but it might take some time. A bit like the International Astronomical Union is in charge of naming planetary features. As an aside, there are still a lot of extraterrestrial volcanoes unnamed!)

Even a volcano with a name can be misleading. For instance, you might think that Bezymianny, in Kamchatka, has a proper name, until you realize that it literally means "unnamed" in Russian!