English equivalent to the Swedish idiom "A dear child has many names"

This strikes me as conveying a similar sentiment:

Victory has a thousand fathers, but defeat is an orphan. Former U.S. President John F. Kennedy

While Kennedy popularized this saying, there is some question concerning priority. For example, this post attributes the saying to Count Galeazzo Ciano, Italian dictator Benito Mussolini's foreign minister and son-in-law, who supposedly recorded it in his diary. Either way, it captures the sentiment that "A dear child has many names." By analogy, "a dear child" corresponds to "a victory" and "many names" corresponds to "many fathers". By the same token, an "unloved child" corresponds to "an orphan", who has no fathers and no names.

I think that what you are looking for is half-way between a proverb (A simple and short saying, widely known, often metaphorical, which expresses a basic truth or practical precept, based on common sense or cultural experience.) and an idiom (An expression that is peculiar to itself grammatically or cannot be understood from the individual meanings of the words.   Quite a few idioms are language specific, and thus difficult to translate.).

In fact, your idiom essentially describes the concept of a proverb.   How meta!   I cannot think of an English equivalent, but I will let my mind work on the problem subconsciously to see if it remembers anything...

What about call it what you will?
This can be both positive and negative:

Call it what you will, bisou, baiser, bacio, kiss or Kuss: in the hot South or the cool North, the kiss is the graceful preliminary to the game of love, a loving gesture or the expression of deep friendship - and always a sensual pleasure.

Hot kisses (from a Linguee search with a German translation. I didn't find the original source.)

"Chance, Destiny, Fate,—call it what you will," cried Gerald, obeying the stronger impulse of his feelings, and clasping her once more to his beating heart.

from the novel The Canadian Brothers by John Richardson (1840).

She said let’s call it quits
Let’s not call it the end of the world
Call it what you will
I’m heartbroken still
Words are just words

from the song Call it What you Will by Joe Pug, 2009.

(As Erik points out in the comments, “Kärt barn har många namn” can be used in a broader sense than just loved children: "for example regarding objects, habits or regional conventions".)

The short answer is 'No'.

This saying, which I first heard from a Swedish friend some years ago, refers to the 'pet names' that parents and other family members give to their children. It does not mean 'alternative formal callings' but affectionate diminutives: nick-names, bynames.

Each of these aliases usually reflects some aspect of the child's personality which is endearing; some milestone in their development; some amusing or in other way remarkable episode. The namings are ways of expressing love for the child, by underlining their uniqueness.

Examples abound in my own family, and now with my own children, but I shall offer none. This is, by the way, known as 'Family Speak' and Nancy Keesing has written of and documented some of it.

I thought the 'Eskimos and snow' myth had been debunked. English has many names for precipitation from the sky: mist, drizzle, downpour, spitting, shower, deluge... These describe the nature of the rain, how it arrives from above. They do not suggest that it is anything other than rain. I understand that the Inuit 'snow' nomenclature is likewise.

'A rose by any other name' is not quite the same thing.

Romeo, Romeo. So how come you're all like 'Romeo' and stuff?

Juliet asks herself why she is so besotted with the name 'Romeo', and realises that she would be just as obsessed were the lad named Tyrell or Dennis. So to speak.

I am from the mid-western United States. To convey this meaning, we would say (Phonetically):
"TOE May Toe, Tah MAH Toe"

Or, if we thought the whole thig was rediculous, we'd change our town to "Pleasantly Dismissive" and say:
"Aaaah, Toe May Toe, Tah Mah too; Puh Tay Toe, Puh Taa Toe."
Usually followed by a hand gesture meaning "Go away now" or "Stop bothering me."

To be fair, Most mid-westerners may not be able to grasp the subtlety of the Swedish Expression.