Lord Subrahmanya is known as Kumaran, Kandan, Murugan, Velan etc. How these names have come?
The names you have listed originated in different langauges namely, Sanskrit and Classical Tamil.
From Monier-Williams Sanskrit-English Dictionary, 1899 (MW for short):
Subrahmaṇya : "su—brahmaṇya very kind or dear to Brāhmans". This epithet is applied to Skanda or Kārttikeya as well as to Viṣṇu and Śiva. Much earlier, duirng the period of the Vedic religion, this was simply the name of a Vedic official: 'one of the three assistants of the Udgātṛ priest' (MW). So this shows that pretty much any god was called subrahmaṇya in the sense they were favorable to the Brāhmans.
Kumaran : This Tamil name is a cognate of Skt. kumāra which we will see next.
Kumāra : This occurs in its etymological sense, and with no connection to Kārttikeya , as early as in the Rig Veda: "a child, boy, youth, son" (MW). During the epic period, in the Mahabharata, it was also applied to Skanda or Kārttikeya meaning "a beautiful youth".
Linguistically this word kumāra is well-known to have a phonological structure alien to Indo- European and to have had origins in a language other than Vedic Sanskrit and borrowed from a substrate language family such as Dravidian.
Kandan : This is a Tamilized version of Skt. skanda.
Skanda: MW gives the meanings: "‘Attacker’, N. of Kārttikeya (son of Śiva or of Agni; he is called god of war as leader of Śiva's hosts against the enemies of the gods ; he is also leader of the demons of illness that attack children".
Murugan: This is an original Tamil or Dravidian word phonologically murukan or muruku both of which are attested as the names of Skanda in the earlliest classical Tamil literature (150 BC).
Vēlan: This early Tamil word is derived from vēl (வேல்) 'dart, spear, lance, javelin'. But surprisingly it only meant the priest who was doing the puja to the God murukan , frenzied and under possession by murukan and not did not mean the God murukan himself even though the God was iconically described as wielding the weapon vēl!
Kartikeya: Because he was brought up by goddesses known as the Krittikas, he came to be called Kartikeya.
Shadanana / Shanmukha / Arumugam: He had six (shada) faces (anana). He was therefore also known as Shadanana or Shanmukha. Arumugam ("six-faced"; Aru = six + Mugam = face).
Kartikeya: having been born of the Krittikas and reared by them, he came to be known throughout the three worlds as Kartikeya.
Skanda: having sprung from the seed which had fallen off from Rudra he was named Skanda
Guha: because of his birth in the solitude of a forest of reeds he came to be called by the name of Guha (the secret-born).
In Mahabharata: Vana Parva: Markandeya-Samasya Parva: Section CCXXX, Yudhishthira asked sage Markandeya about different names of Kartikeya.
Vaisampayana continued, "Thus addressed by the Pandava in that assembly of Rishis, the worshipful Markandeya of high ascetic merit replied,
Agneya (Son of Agni),
Diptakirti (Of blazing fame),
Anamaya (Always hale),
Dharmatman (The virtuous-souled),
Bhutesa (The lord of all creatures),
Mahishardana (The slayer of Mahisha),
Kamajit (The subjugator of desires),
Kamada (The fulfiller of desires),
Kanta (The handsome),
Satyavak (The truthful in speech),
Bhuvaneswara (The lord of the universe),
Sisu (The child),
Sighra (The quick),
Suchi (The pure),
Chanda (The fiery),
Diptavarna (The bright-complexioned),
Subhanana (Of beautiful face),
Amogha (Incapable of being baffled),
Anagha (The sinless),
Rudra (The terrible),
Priya (The favourite),
Chandranana (Of face like the moon),
Dipta-sasti (The wielder of the blazing lance),
Prasantatman (Of tranquil soul),
Bhadrakrit (The doer of good),
Kutamahana (The chamber of even the wicked),
Shashthipriya (True favourite of Shashthi),
Pavitra (The holy),
Matrivatsala (The reverencer of his mother),
Kanya-bhartri (The protector of virgins),
Vibhakta (Diffused over the universe),
Swaheya (The son of Swaha),
Revatisuta (The child of Revati),
Prabhu (The Lord),
Neta (The leader),
Visakha (Reared up by Visakha),
Naigameya (Sprang from the Veda),
Suduschara (Difficult of propitiation),
Suvrata (Of excellent vows),
Lalita (The beautiful),
Valakridanaka-priya (Fond of toys),
Khacharin (The ranger of skies),
Brahmacharin (The chaste),
Sura (The brave),
Saravanodbhava (Born in a forest of heath),
Viswamitra priya (The favourite of Viswamitra),
Devasena-priya (The lover of Devasena),
Vasudeva-priya (The beloved of Vasudeva), and
Priya-krit (The doer of agreeable things)
--these are the divine names of Kartikeya. Whoever repeateth them, undoubtedly secureth fame, wealth, and salvation."