Short answer
– Psalm 136 is anonymous in the Hebrew text (no superscription). From an evangelical scholarly perspective the most likely human composer is unknown; the best explanation is that it is a liturgical/Levitical thanksgiving hymn compiled for corporate worship, probably written or shaped during the post‑exilic/temple period. Evangelicals also stress that, whatever the human composer, the psalm is divinely inspired.

Why scholars (including many evangelicals) say the human author is unknown or a temple worship leader
– No heading: Unlike many psalms that carry a “Of David” or other ascription, Psalm 136 has no authorial superscription in the Hebrew.
– Liturgical form: The psalm’s distinctive feature is the constant refrain, “for his steadfast love (hesed) endures forever,” which closes every verse. That strong call‑and‑response pattern fits corporate worship, suggesting it was used by temple musicians or a chorus and probably composed by someone in the worship establishment (a Levite, temple singer, or liturgical compiler).
– Sweeping historical sweep: The psalm runs through creation, the exodus, God’s acts toward Israel and nations — a kind of compact national thanksgiving. That theological summary style is typical of liturgical thanksgiving hymns and collections formed in or after Israel’s exile when remembering God’s saving acts was important to corporate identity.
– Language and theology: The repeated emphasis on hesed and the doxological form links it with Israel’s cultic thanksgiving traditions; some commentators see post‑exilic editorial shaping (though not everyone insists on a late date).

How this fits an evangelical outlook
– Inspiration and authority: Evangelicals affirm that the Bible is inspired by the Holy Spirit. Even if the human author is unknown, Psalm 136 is Scripture and speaks with divine authority about God’s steadfast love.
– Worship and Christological reading: Evangelical preachers typically use this psalm to emphasize God’s unchanging covenant love (hesed) made visible in salvation history and to point forward to Christ’s work (God’s saving acts find their fulfillment in Jesus). The psalm’s repetitive refrain works well as a congregational affirmation of God’s mercy.
– Practical application: Evangelicals often highlight the psalm’s call to grateful remembrance — thanking God for creation, deliverance, provision, and rule — and encourage using it in personal and corporate praise.

Representative evangelical commentaries and further reading
– Derek Kidner, Psalms 73–150 (Tyndale Commentary) — helpful, pastoral, evangelical.
– Tremper Longman III, The Book of Psalms (in some evangelical series) and other works on the Psalms.
– John Goldingay, Psalms (3 vols., Baker/IVP) — broadly evangelical and scholarly.
– Expositor’s Bible Commentary / NIV Application Commentary entries on Psalms — for accessible evangelical treatments.

Short summary
Psalm 136 most likely has no identified human author; it appears to be a liturgical thanksgiving hymn used in Israel’s worship, probably crafted or compiled by someone in the temple tradition (a Levite or worship leader), perhaps with post‑exilic shaping. From an evangelical standpoint, that human anonymity does not weaken the psalm’s authority; it remains Scripture that powerfully proclaims God’s enduring hesed and calls the people to thankful praise.