The words subjunctive (from Latin subiunctivus, "connective, subordinating") and conjunctive (from Latin coniunctivus, "connective") normally mean exactly the same thing and refer to exactly the same mood, as far as different languages can be compared. In modern English, conjunctive is seldom heard; it is normally always subjunctive. So it would make perfect sense to call the German Konjunktiv in English subjunctive, if you must use an English word. If you use a German word, however, the only option is Konjunktiv.
It should be noted that Proto-Indo-European probably had two separate moods, conjunctive/subjunctive and optative ("expressing a wish"). Both moods were still present in classical Greek; but they had fused into one mood in (Pre-)Latin, which only had a conjunctive/subjunctive that did the work of both. In (Proto-)Greek, the optative was mainly marked by /i/, whereas the conjunctive/subjunctive was marked by a lengthening of the theme vowel. The unified successor mood that emerged in most Indo-European languages acquired various other formal properties.
It should also be noted that both moods already had several, quite different functions each in Greek, so that their names are not very accurate descriptions if one considers what they mean in Latin—nor could there be accurate names for such complex moods.
The Latin names of the mood, coniunctivus and subiunctivus, were both used from late Antiquity onwards. Among the modern languages, some use a form of coniunctivus, some subiunctivus, and some both. The Oxford English Dictionary (2nd ed.) explains it quite well for Latin and English:
Both modus conjunctīvus and m. subjunctīvus were used by the Latin Grammarians of the 4th c. Isidore Orig. i. viii. 4 (a 640) has only conjunctīvus, ‘quia ei conjungitur aliquid, ut locutio plena sit’. Littré cites subjonctif ou conjonctif from Meigret 1550. In English use Subjunctive was the usual name until comparatively recent times. It is now used by some in a narrower sense than Conjunctive: see quot. 1871.
- 1730–6 Bailey (folio), The Conjunctive (or Subjunctive) Mood of a Verb.
- 1755 Johnson, Conjunctive, adj..(In grammar.) The mood of a verb, used subsequently to a conjunction.
- 1824 L. Murray Eng. Gram. (ed. 5) I. 152 Some grammarians apply, what is called the conjunctive termination, to the persons of the principal verb, and to its auxiliaries, through all the tenses of the subjunctive mood.
- 1871 Publ. Sch. Lat. Gram. 96 The Conjunctive Mood is for conceptive statement: as gaudeam si absit. When this Mood appears in principal construction, we call it the pure conjunctive, as gaudeam: when it depends on another Verb, it is called Subjunctive, as absit.
- Ibid. 167 Examples of the Conjunctive Mood used Subjunctively.
The interwiki links from the English Wikipedia page Subjunctive nicely show how the languages are split between both terms. Some of these languages might use both terms.
- Bahasa Indonesia - Modus subjungtif;
- 中文 (Chinese) - Traditional 虛擬語氣, Simplified 虚拟语气.
- Croatian - Hrvatski konjunktiv, aorist i kondicional;
- Czech - Konjunktiv;
- Danish - Konjunktiv;
- Dutch - Aanvoegende wijs;
- Esperanto - Subjunktivo;
- Finnish - Subjunktiivi;
- French - Subjonctif;
- German - Konjunktiv;
- Icelandic - Viðtengingarháttur;
- Ido - Subjuntivo;
- Italian - Congiuntivo;
- Japanese - 接続法;
- Latina - Coniunctivus;
- Magyar - Kötőmód;
- Norwegian - Konjunktiv;
- Polish - Tryb łączący;
- Portuguese - Modo subjuntivo;
- Romanian - Conjunctiv;
- Russian - Сослагательное наклонение;
- Spanish - Modo subjuntivo;
- Swedish - Konjunktiv;
- Walon - Suddjonctif;