The name Nila-Lohita illustrates the dual form of Lord Shankara, comprising dominated (Prakriti) and dominating (Purusha) factors. Shiva is called as Nila-Lohita for his mixed complexion of blue and red colors. Out of his eightfold deities, in fact Nila-Lohita indicates his fiery deity because fire-flames display red and black colors in upper and lower portions respectively. Shankara is the direct deity of fire, so he is known as Nila-Lohita नीललोहित.
Ardha-Narishwar अर्धनारीश्वर form, which means a form with half man and half woman put together, can also be understood by the name Nila-Lohita. Shiva has a fairly golden complexion like camphor and Goddess Kali’s hue is like blue colored Atasi flower. When Lord Shankara places Goddess Bhagwati at half space of his body, then a reddishness appears there due to contact of golden and blue colors. The blackish complexion of Kali also gets repressed and turns into bluish and thus Shankara becomes Nila-Lohita.
At some places the secret of Nila-Lohita is explained for a combination of bluish neck and reddish face of Lord Shiva. Shiva becomes Nila-Lohita due to his red and blue outlook. The Upanishads describe that the fire and moon have a combine look like Nila-Lohita.
Puranas state that Brahma ji did a sacrifice to attain Shiva as his son. Perspiring drops of blue and red colors came out due to heat of fire-sacrifice. Rudra got manifested from these drops and thus he was called Nila-Lohita. Bhaskar Roy explains the meaning of Nila-Lohita as under—
नेमाङ्गनं प्रकृतिपुरुषं रवेरन्तश्व रूपयुगपद्वपुस्तव्।
वेधोऽलिकाम्बुकणतोऽरुणासिताज्जातः शिव! त्वमिति नीललोहितः॥
Ignorance is mentioned as blue and knowledge is red in spiritual science. Shiva is the destroyer of ignorance, so he is Nila-Lohita.