Utsaṅga (Utsanga) is one of the thousand and eight names of God Śiva (Siva). The scholar Haridāsa Siddhāntavāgīśa, in his Bhāratakaumudī ṭīkā (Bharatakaumudi Tika)says that —
utkṛṣṭo saṅgo yasya sa utsaṅgaḥ.
A divine sense of intimacy with the Supreme God gives bliss, knowledge and peace to human heart. In this sense, Śiva is known as Utsaṅga.
Nīlakaṇṭha (Nilakantha), in his Bhāratabhāvadīpa ṭīka (Bharatabhavadipa tika)says that — utsaṅgaḥ asaṅgaḥ.
Utsaṅga means beyond proximity or relation. It refers to one who has overcome all mortal desires and relations. God Śiva is conceptualised as a sannyāsī(sannyasi) — a recluse who is beyond all worldly connections. S he is called Utsaṅga.
Another meaning of Utsaṅga is ‘lap’ . Śiva can also be called so because he holds the whole universe under his care — as if,  in his lap.