Not only in Shiva Sahasranama stotra, Vedas also call Lord Shiva by the name "Shikhandi". So it is a name which is from Vedas given to Lord Shiva:
अपश्यमस्यन्तं रुद्रं नीलग्रीवं शिखण्डिनम् ।।१ ।। नमो ऽस्तु नीलशिखण्डाय सहस्राक्षाय वाजिने । (AtharvaVeda Paipplada Samhita 14.3, 14.4)
apaśyamasyantaṃ rudraṃ nīlagrīvaṃ śikhaṇḍinam ।।1 ।। namo 'stu nīlaśikhaṇḍāya sahasrākṣāya vājine ।
I saw Rudra, Nilagriva, Shikhandin. Salutation to NilaShikhandi, Sahasraksha (with 1000 eyes)
King Drupada was a devotee of Lord Shiva and was childless and he got the child Shikhandi by doing Shiva Upasana:
दुर्योधन उवाच।
कथं शिखण्डी गाङ्गेय कन्यां भूत्वा पुरा तदा।
पुरुषोऽभूद्युधिश्रेष्ठ तन्मे ब्रूहि पितामह ।।
भीष्म उवाच।
भार्या तु तस्य राजेन्द्र द्रुपदस्य महीपतेः।
महिषी दयिता ह्यासीदपुत्रा च विशांपते ।।
एतस्मिन्नेव काले तु द्रुपदो वै महीपतिः।
अपत्यार्थे महाराज तोषयामास शङ्करम् ।।
अस्माद्वधार्थं निश्चित्य तपो घोरं समास्थितः।
ऋते कन्यां महादेव पुत्रो मेस्यादिति ब्रुवन् ।।
भगवन्पुत्रमिच्छामि भीष्मं प्रतिचिकीर्षया ।
इत्युक्तो देवदेवेन स्त्रीपुमांस्ते भविष्यति ।।
निवर्तस्व महीपाल नैतञ्जात्वन्यथा भवेत् ।
स तु गत्वा च नगरं भार्यामिदमुवाच ह ।।
कृतो यत्नो महादेवस्तपसाऽऽराधितो मया ।
कन्या भूत्वा पुमान्भावी इति चोक्तोस्मि शंभुना ।।
पुनः पुनर्याच्यमानो दिष्टमित्यब्रवीच्छिवः ।
नतदन्यच्च भविता भवितव्यं हि तत्तथा ।। (Mahabharata Udyoga parva chapter 188)
"Duryodhana said, 'Tell me, O grandsire, how Sikhandin, O Ganga's son, having before been born a daughter, afterwards became a man, O foremost of warriors.' "Bhishma said, 'O great king, the eldest and beloved queen of king Drupada was, O monarch, childless (at first). During those years, king Drupada, O monarch, paid his adoration to the god Sankara for the sake of offspring, resolving in his mind to compass my destruction and practising the austerest of penances. And he begged Mahadeva, saying, 'Let a son, and not a daughter, be born unto me. I desire, O god, a son for revenging myself upon Bhishma.' Thereupon, that god of gods said unto him, 'Thou shalt have a child who will be a female and male. Desist, O king, it will not be otherwise.' Returning then to his capital, he addressed his wife, saying, 'O great goddess, great hath been the exertion made by me. Undergoing ascetic austerities, I paid my adorations to Siva, and I was told by Sambhu that my child becoming a daughter (first) would subsequently become a male person. And though I solicited him repeatedly, yet Siva said,--This is Destiny's decree. It will not be otherwise. That which is destined must take place!'
When the child (daughter) was born then she was named by Drupada himself by the name Shikhandi. It is natural to think that one would give the name of Lord Shiva to the child who was born through Shiva Kripa:
श्रद्दधानो हि तद्वाक्यं देवस्याच्युततेजसः।
छादयामास तां कन्यां पुमानिति च सोब्रवीत् ।।
जातकर्माणि सर्वाणि कारयामास पार्थिवः।
पुंवद्विधानयुक्तानि शिखण्डीति च तां विदुः ।।
अहमेकस्तु चारेण वचनान्नारदस्य च।
ज्ञातवान्देववाक्येन अम्बायास्तपसा तथा ।। (Udyoga parva chapter 188)
Believing these words of that deity of unfading energy, he too concealed the real sex of his child, saying,--She is a son. And, O king, Drupada caused all the rites of infancy, prescribed for a son, to be performed in respect of that child, and he bestowed the name of Sikhandi on her. I alone, through my spies and from Narada's words, knew the truth, informed as I previously was of the words of the god and of the ascetic austerities of Amva!'"
Later she transforms into a male by the power of a Yaksha. Now one may ask why the particular name 'Shikhandi' was given and no other name. There may not be a precise answer to explain this. But if we look at other Vedic names of Lord Shiva we find most names ending in 'Akara' like "Tryambaka", "Ishana", "Hara", "Rudra", "Shankara", "Mahadeva", "Shiva", "Bhava", "Sarva", etc... But the name "Shikhandi" ends in "Ikara" and it can be used as feminine too (with dirgha I). Since she was a daughter and King Drupada was portraying her as a son, the name "Shikhandi" might best fit as it is the name of Lord Shiva also and can also be used as a feminine name. As Bhishma himself says in Udyoga Parva:
व्रतमेतन्मम सदा पृथिव्यामपि विश्रुतम् ।
स्त्रियां स्त्रीपूर्वके चैव स्त्रीनाम्नि स्त्रीसरूपिणि ।।
न मुञ्चेयमहं बाणमिति कौरवनन्दन ।
न हन्यामहमेतेन कारणेन शिखण्डिनम् ।। (Udyoga parva chapter 192)
Even--this is my vow, known over all the world, viz.,
that I will not, O son of Kuru's race, shoot weapons upon a woman, or one that was a woman before or one bearing a feminine name, or one whose form resembleth a woman's. I will not, for this reason, slay
Sikhandin. Even this, O sire, is the story that I have ascertained of Sikhandin's birth.
Shikhandi nahusho vrushaha
Shikhandi is the name for Shriman Narayana in Vishnusahastranaam which means Lord who Peacock feathers.