"She told us he would never be able to get a job, and that teachers wouldn’t want to teach him. 'I tried to explain that we are not religious people, and Lucifer in Greek means "light-bringer" and "morning" but she wouldn’t listen.'"

Says a father quoted in "HELLUVA NAME/Couple win battle to name son Lucifer after registrar tried to bar them because it is another name for the devil" (The Sun).

[Dan Sheldon] 37, a plant hire company boss, lodged an official complaint over how he and Mandy, 32, were treated at their local office in Chesterfield, Derbys. He said: “We were really excited to go and get him registered but the woman looked at us in utter disgust.... She even told us that it was illegal to name a child that in New Zealand and that maybe we could name him something else but refer to him as Lucifer at home....”

Chesterfield is in England.

“We were gobsmacked with her behaviour. Eventually she did it, but it was through gritted teeth. Honestly, we just thought it was a nice name . . . a unique one. We didn’t expect to get so much grief about it.”

Derbyshire County Council said: “We apologise if they were offended but it is the job of our registrars to advise in these matters as sometimes people are not aware of certain meanings or associations around certain names.”

So the problem here is not that the parents wanted to name their child Lucifer, but that the government official gave them any friction at all. The name was registered, the parents made an official complaint against the government worker, and the county council apologized.

From the Wikipedia article, "Lucifer":

The motif of a heavenly being striving for the highest seat of heaven only to be cast down to the underworld has its origins in the motions of the planet Venus, known as the morning star. The Sumerian goddess Inanna (Babylonian Ishtar) is associated with the planet Venus.... A similar theme is present in the Babylonian myth of Etana...

The brilliancy of the morning star, which eclipses all other stars, but is not seen during the night, may easily have given rise to a myth such as was told of Ethana and Zu: he was led by his pride to strive for the highest seat among the star-gods on the northern mountain of the gods ... but was hurled down by the supreme ruler of the Babylonian Olympus....

In classical mythology, Lucifer ("light-bringer" in Latin) was the name of the planet Venus, though it was often personified as a male figure bearing a torch.... He was often presented in poetry as heralding the dawn....

In the Book of Isaiah, chapter 14, the king of Babylon is condemned in a prophetic vision by the prophet Isaiah and is called הֵילֵל בֶּן-שָׁחַר (Helel ben Shachar, Hebrew for "shining one, son of the morning")... According to the King James Bible-based Strong's Concordance, the original Hebrew word means "shining one, light-bearer", and the English translation given in the King James text is the Latin name for the planet Venus, "Lucifer", as it was already in the Wycliffe Bible.

However, the translation of הֵילֵל as "Lucifer" has been abandoned in modern English translations of Isaiah 14:12. Present-day translations render הֵילֵל as "morning star"... "daystar"...  "shining one"...  or "shining star"...

In a modern translation from the original Hebrew, the passage in which the phrase "Lucifer" or "morning star" occurs begins with the statement: "On the day the Lord gives you relief from your suffering and turmoil and from the harsh labour forced on you, you will take up this taunt against the king of Babylon: How the oppressor has come to an end! How his fury has ended!" After describing the death of the king, the taunt continues"

How you have fallen from heaven, morning star, son of the dawn! You have been cast down to the earth, you who once laid low the nations! You said in your heart, 'I will ascend to the heavens; I will raise my throne above the stars of God; I will sit enthroned on the mount of assembly, on the utmost heights of Mount Zaphon. I will ascend above the tops of the clouds; I will make myself like the Most High.' But you are brought down to the realm of the dead, to the depths of the pit. Those who see you stare at you, they ponder your fate: 'Is this the man who shook the earth and made kingdoms tremble, the man who made the world a wilderness, who overthrew its cities and would not let his captives go home?'...

Isaiah 14:12 became a source for the popular conception of the fallen angel motif seen later in 1 Enoch 86–90 and 2 Enoch 29:3–4. Rabbinical Judaism has rejected any belief in rebel or fallen angels... An association of Isaiah 14:12–18 with a personification of evil, called the devil developed outside of mainstream Rabbinic Judaism in pseudepigrapha and Christian writings, particularly with the apocalypses.

Some Christian writers have applied the name "Lucifer" as used in the Book of Isaiah, and the motif of a heavenly being cast down to the earth, to Satan. Sigve K Tonstad argues that the New Testament War in Heaven theme of Revelation 12 (Revelation 12:7–9), in which the dragon "who is called the devil and Satan … was thrown down to the earth", was derived from the passage about the Babylonian king in Isaiah  Origen (184/185 – 253/254) interpreted such Old Testament passages as being about manifestations of the devil; but writing in Greek, not Latin, he did not identify the devil with the name "Lucifer". Origen was not the first to interpret the Isaiah 14 passage as referring to the devil: he was preceded by at least Tertullian (c. 160 – c. 225), who in his Adversus Marcionem (book 5, chapters 11 and 27) twice presents as spoken by the devil the words of Isaiah 14:14: "I will ascend above the tops of the clouds; I will make myself like the Most High". Though Tertullian was a speaker of the language in which the word "lucifer" was created, "Lucifer" is not among the numerous names and phrases he used to describe the devil. Even at the time of the Latin writer Augustine of Hippo (354–430), a contemporary of the composition of the Vulgate, "Lucifer" had not yet become a common name for the devil.

Some time later, the metaphor of the morning star that Isaiah 14:12 applied to a king of Babylon gave rise to the general use of the Latin word for "morning star", capitalized, as the original name of the devil before his fall from grace, linking Isaiah 14:12 with Luke 10 (Luke 10:18) ("I saw Satan fall like lightning from heaven") and interpreting the passage in Isaiah as an allegory of Satan's fall from heaven.

As a result, "Lucifer has become a byword for Satan or the devil in the church and in popular literature", as in Dante Alighieri's Inferno, Joost van den Vondel's Lucifer, and John Milton's Paradise Lost. However, unlike the English word, the Latin word was not used exclusively in this way and was applied to others also, including Jesus: the Latin (Vulgate) text of Revelation 22:16 (where English translations refer to Jesus as "the bright morning star") has stella matutina, not lucifer, but the term lucifer is applied to Jesus in the Easter Exultet and in a hymn by Hilary of Poitiers that contains the phrase: "Tu verus mundi lucifer" (You are the true light bringer of the world)....

John Calvin said: "The exposition of this passage, which some have given, as if it referred to Satan, has arisen from ignorance: for the context plainly shows these statements must be understood in reference to the king of the Babylonians." Martin Luther also considered it a gross error to refer this verse to the devil.