In Iran there is another way to do the mandatory military service and it is working for a governmental organization or company instead. It is simply called 'امریه' in Persian. Is it called CPS (Civilian Public Service)? Civilian Military Service? what exactly?
The programs that now and previously existed in Germany, Finland, and elsewhere are commonly translated as national service or some variation thereof (e.g. universal national service, mandatory national service). This term may be applied to mandatory military service (e.g. the Greek Embassy's page on “National Service Information”), to both military and civilian service (e.g. Singapore's National Service), and sometimes strictly to so-called alternative service (or substitute service) pathways for those who do not qualify for mandatory military service.
In the U.S., editorials both in favor of and against the creation of such programs similarly use national service. Due to the historical absence of this institution in the U.S. and U.K., however, it may not be understood out of context.
For that matter, mandatory military service, known as conscription and colloquially referred to as the draft, has also a rarity in in the modern U.S. and U.K., especially in peacetime. In the U.S., males aged 18 through 25 must register for potential conscription, but no one has been called up since the Selective Service System was reinstated in the 1970s.
During the Second World War, conscientious objectors facing the draft were given the opportunity to provide alternate national service through the Civilian Public Service. This program was discontinued after the war, however, and its name is not a suitable synonym.
Back in my day the US Selective Service System (conscription, "the draft") provided for two Conscientious Objector statuses: available for non-combatant military service), available for alternate community service).
The present classifications seem to be more complicated; but it appears that if the draft is ever revived qualifying registrants will be required to perform alternative service.
These are distinct from occupational deferments, under which registrants in certain vital occupations will not be inducted ("called up" or "Greetingsed" as we used to call it).
That is not something that exists in every country/state in the world. It does not exist in England and the rest of the UK. There is an English word for mandatory military service, which is conscription. See the entry at CDO. The UK used to have conscription until the 1960s. While there is a word for mandatory military service, there is no particular way of referring to a civilian equivalent of it.
If you want to refer to it in English, it is probably best to use a description of it, like you have in your question.