"Say My Name" is a minimal electropop song with a prominent ukulele riff that Styrke convinced Loelv to integrate as a central part.

She described the song as musically and lyrically different from the material of her previous studio album Kiddo (2015), and explained that working with Loelv helped her evolve her sound.

The song's accompanying music video, directed by Daniel Skoglund, portrays the singer in colorful and simple sets with infinity mirror effects.

For her third studio album Sway (2018), Tove Styrke wanted to "strip down production" while keeping the songs "interesting" with "[their] own I.D.[s]".

[1] In the summer of 2016, Styrke met with Elof Loelv and Tinashe "T Collar" Sibanda for a session that resulted in "Say My Name" being written.

[3] Initially, Loelv presented the song's eventual bass line, which made Styrke burst into laughter as "it wasn't even a beat, it was two notes", she revealed to Out.

[2][4] Loelv came up with the ukulele riff by accident and was reluctant to include it, but Styrke liked it and had to convince him to integrate it as a central part of the track.

[7] In an interview for Time, she described "Say My Name" as "like a starting point of a new era", and further elaborated on working with Loelv, "I had been writing a lot prior to that, but it wasn't until I met Elof that it really clicked for me.

"[2] Styrke explained that the song differs from the material of her second studio album Kiddo (2015), which was "all about being loud and big", whereas "Say My Name" is "close and simple".

[3][8][9][10] Erica Russell, writing for PopCrush, said the track includes "a textural, strummy string riff and a follow-the-bouncing-ball beat".

[14] Writer Issy Beech of Noisey viewed the track as "bouncing" and "offbeat",[8] while Idolator's Mike Wass noted a change of pace from Kiddo, writing that Styrke "explores a warmer, more organic soundscape".

"[16] Styrke said to Pigeons & Planes that selecting "Say My Name" as the lead single for Sway was a "no-brainer", stating that "it really raised the bar in every way".

Issy Beech, writing for Noisey, wrote positively of the song and complimented the lyrical content, arguing that "[Styrke] has practically bottled warm weather and lust for life.

"[8] Mike Wass of Idolator viewed the single as "devastatingly catchy",[13] and Variance's Lindsay Howard described it as a "glossy, summery cut".

[26] Thomas Smith of NME opined that the song "oozes confidence and a star power that is ready to permeate and resonate with a wider audience".