Persian/Iranian names of the planets

Sun
-Xôršîd / Hôršîd, from Middle Persian Xwar(x)šēd, (indirectly) from Avestan Hvarə.xšaēta, "radiant Sun (Hvar)"
-Hûr (poetic), from the non-compound version of the same name (Old Persian Hvar)
-Mehr, from Middle Persian Mihr, from Old Persian Miθra/Mitra
-Âftâb, "sun, sunshine", from Middle Persian āftāb
-*Hormoz. See on Jupiter and the first note below.
Mercury
-Tîr, from Middle Persian Tīri, from Old Persian Tīriya; translating Syriac Nebū or late Akkadian Nabû, from earlier Akkadian Nabium
-Otâred, from Classical Arabic ʿUṭārid
Venus
-(A)nâhîd, from Middle Persian Anāhīd, from Old Persian Anahita; translating Syriac ˀEštrā / ˀEstrā, borrowed from Akkadian Ištar (or the Akkadian directly)
-Zohre, from Classical Arabic Zuhara
Moon
-Māh / Mah, from Middle Persian Māh, from Old Persian Māha
Mars
-Bahrâm, from Middle Persian Wahrām / Wahahrān, not found in Old Persian, from Avestan Vərəθraγna; translating Syriac (Akkadian?) Nergal / Nerig, from earlier Akkadian Nerigal / Nerigla
-Merrîx, from Classical Arabic Mirrīḵ
Jupiter
-Hormoz / Hurmoz / Hormazd / Hurmazd / Urmazd, from Middle Persian Ōhrmazd / Hormozd, from Old Persian Ahura Mazda; translating late Akkadian/Syriac (from Akkadian) Bēl, which (largely) replaced earlier Akkadian Mar(u)duk
-Moštarî from Classical Arabic Muštarī
-Berjîs, from Classical Arabic Barjīs (rare alternative to Muštarī), but could also be an Iranian word
-Zâvoš / Zâvûš, (not from Avestan dyaoš but) from Arabic Zāwūš (e.g. in the 10th-century CE Ghāyat al-Hakīm, p. 196 in Ritter-Plessner's edition), from Greek Zeus (via Syriac?)
Saturn
-Keyvân, from Middle Persian Kēwān, from Syriac Kewwān (Kēwān?), or late Akkadian Kaiwān, from earlier Akkadian Kayamānu
-Zohal, from Classical Arabic Zuḥal
Uranus
-Urânus, from common European Uranus, from Latin Ūranus, from Ancient Greek Ouranos
Neptune
-Neptun, from common European Neptun-, from Latin Neptūnus
Pluto
-Pluton, from common European Pluto(n), from Latin Pluto(n)-, from Ancient Greek Ploutōn

Note on Ahura Mazda as a solar name:
In western Iranian languages, this is a name of Jupiter, but in some eastern ones, already at the time of the Kushan empire (Bactrian Ooρoμoζδο Ōromozdo), but still today in the Zebaki and Ishkashimi languages (as Ōrmōzd and Rēmuz, respectively) of the Pamir Mountains (Wilhelm Eilers, "Sinn und Herkunft der Planetennamen"). This has been taken as evidence of either Ahura Mazda having been a solar god in the pre-Zoroastrian Iranian religion supposedly preserved in the East, or of non-Zoroastrian Iranians syncretizing Ahura Mazda and the sun. Neither theory is convincing or necessary: just as other Iranian languages of the same region have descendants of Miθra as their word for the sun, an association that took place within Zoroastrianism but never reduced Miθra to purely a solar god, and association of Ahura Mazda with Jupiter within Zoroastrianism obviously never reduced him to a Jovian god, so association of the sun with Ahura Mazda says something about the status of the sun for some eastern Iranians, namely as the most important of the planets, but not very much about the theology of Ahura Mazda. Comparison can easily be made with Greco-Roman identifications of sun and Jupiter/Zeus, similarly resulting from a feeling that the most important god should be associated with the most important planet. In general, planetary associations tend to be superadded to a deity's existing imagery and attributes rather than replacing them.

General Notes:
Some combination of these names is used in the various Iranian languages, as well as by Parsis (or until relatively recently, at least). For Zoroastrians, some of these continue to be thought of as gods (and for some Muslims, something very like gods).
Persianate names
The Persianate names, except for Hur/Hôršîd and Māh, were originally non-planetary divine names; Miθra became increasingly understood as a solar god, while the others came to their planetary meaning by an interpretatio iranica of the Akkadian(=Babylonian) names of the planets:
The god of Mercury was a patron of scribes, the Venus goddess's domain was love, Mars's god had to be warlike, Jupiter's name was that of the supreme god, and Saturn, finally, was simply taken over as a loanword. Notably, the technical, scientific name, not the divine name (Ninurta) was taken over here, apparently because it was more widely in use.
As in the Latinate and Greek-speaking world, the convention of naming the planets after deities held firm for a very long time, until today even, and was also known to Arabs and, through the Picatrix, the Latin version of the Ghāyat al-Hakīm, the Persian planetary names even became known in medieval Europe: Maher, Tyr, Anyhyt, Mehe, Baharam, Bargis, Keyhven.
For Zoroastrians and Persian-speaking philosophers, astrologers and esotericists, the planets continued to be quite important, and the 17th century Adhar Kayvani sect even argued that Zarathushtra's teachings were largely allegorical, whereas the worship of the planets (under their Persian as well as other names) was one of the central elements of the ancient Iranian religion they claimed to be resurrecting.
Arabic names
The Arabic names were adapted (perhaps to avoid the older "pagan" names) due to Islamization, but never fully replaced the Iranian names. Before Islam, the Arabs considered the planets to be gods, and the Qurˀan still considers them to be living beings. So does the Greek philosophical and esoteric tradition that entered Islamic culture. The planets became, in the monotheistic imaginary, the primary objects of pagan and idolatrous worship, which accorded with (and further stimulated, even justified) the focus on the planets in remaining pagans and among the Mandaeans. As esoteric Muslim texts like the Ghāyat al-Hakīm or the earlier Epistles of the Brethren of Purity or the popularity of the non-Islamic Nabataean Agriculture show, there was no clear boundary between engaging with the planets (and other celestial bodies) in a monotheistic framework and transgressing it. These and similar texts often treat pagan traditions as authoritative.
European names
Uranus, Neptune and Pluto were adapted, somewhat inconsistently, from Greek and Latin along the lines of the classical names of the other planets by European scientists, and then adapted as loan words into Near Eastern languages.

Greek forms (identifications):
Old Persian Miθra: Mithras/Mithrēs (Hēlios, Apollōn)
Middle Persian Tīri: (Hermēs)
Akkadian/Syriac Nabû: (Hermēs), in the Septuagint (via Hebrew) Nebō
Old Persian Anahita: Ana(h)itis (Artemis, Aphroditē, Mētēr Theōn)
Syriac ˀEstrā (or a similar form): Atharē [if that is not a form of Astartē]
Avestan Vərəθraγna (rather, Parthian Warθraγna): Artagnēs (Hēraklēs, Arēs)
Syriac Nergal: (Hēraklēs), in the Septuagint (via Hebrew) Nērig
Old Persian Ahura Mazda: Ōromasdēs / Ōromazēs (Zeus)
Akkadian/Syriac Bēl: Bēl(os) (Zeus, Kronos, Zeus Kronos[?])
Late Akkadian Kaiwān: in the Septuagint (via Hebrew) in various corrupt forms (Raiphan, Rompha, etc) based on a misreading of the Hebrew texts

Good and evil planetary gods:
There is a late ancient or medieval Zoroastrian myth (preserved in Middle Persian) that claims the planets were originally creations of the evil Ahriman (Aŋra Mainyu), later brought under Ōrmazd's (Ahura Mazda's) control, who himself began to rule over the planet Jupiter and set up other stars as rulers over the other planets:
Mercury: Tīr → Tištrya (=Sirius)
Mars: Wahrām → Vanant (=Altair?)
Jupiter: Mūš par (a demon) → Ōrmazd
Venus: Anahit → Satavaēsa (=Vega?)
Saturn: Kēvān → Haptō-iringa (=Fomalhaut?)
What reason(s) prompted the vilification of the planets is not easy to say; it is clear, however, that it was never universally accepted.
The moon, incidentally, is called Gōcihar in this myth. (Ulla Koch-Westenholz, "Mesopotamian Astrology"). In a variant list (preserved in Gujarati), Ōrmazd is replaced by Majdadāta (= Middle Persian Mazdadāt) as overseer of Jupiter, and Khursēḍa (= New Persian Xūršēd) and Muha (= New Persian Māh) are added to the number of the "good" planetary gods. (Scheftelowitz, Die Entstehung der Manichäischen Religion und des Erlösungsmysteriums")