This doesn't exist word-for-word in canonical scripture - but this verse
“By repeating the name of Śiva, one crosses saṃsāra and attains union/sāyujya with Him.”
is a modern devotional compilation and not a direct citation. these ideas
Constant repetition of “Śiva” gives mokṣa
Name of Rudra is a “boat” across saṃsāra
Attains Śiva-sāyujya
Rudra removes saṃsāra / death
Are all individually present in scripture.
https://upanishads.org.in/upanishads/9/3/8
श्वेताश्वतरोपनिषद्तृतीयोऽध्यायःVerse ८
Verse
वेदाहमेतं पुरुषं महान्तमादित्यवर्णं तमसः परस्तात्।
तमेव विदित्वातिमृत्युमेति नान्यः पन्था विद्यतेऽयनाय॥
Transliteration
vedāhametaṁ puruṣaṁ mahāntamādityavarṇaṁ tamasaḥ parastāt |
tameva viditvātimṛtyumeti nānyaḥ panthā vidyate'yanāya ||
I have realized this Great Being who shines effulgent like the sun beyond all darkness. One passes beyond death only on realizing Him. There is no other way of escape from the circle of births and deaths.
the deity of svetashvatara upaanishad is of course Siva.