The best bit: They recursively reference the paper to provide proof that too many parents choose the same common names:
> For instance, a parent might anticipate the name “Kate” would be a pleasantly traditional yet unique name with only moderate popularity. They would be wrong [6].
Sketch of a more complete solution, excluding shortened forms and very foreign ones. Alternatives are in rough order of frequency.
vowel 0: E, Ye, Je, Ai. Optional and rare; Ai in particular is very rare.
consonant 1: C, K, G, Q. Mandatory; G and Q are rare.
vowel 1: a, aa, ai; optional h or gh. Mandatory. A few shortened forms use i instead.
consonant 2: t, tt, d. Almost mandatory, but a few r-centric variants lack it. There also seem to be a few
vowel 2: a, e. Optional, only valid if consonant 2 exists. In shortened forms, also i, ie, or y; this is the end.
consonant 3: r, l. Optional. Sometimes L starts a new word instead.
vowel 3: i, y, ee, ie, ii, e if no consonant 2, plus several rare vowel sequences. Almost mandatory (assuming consonant 3), but a few rare variants pack the r right next to the n.
consonant 4: n, nn, nh. Optional.
vowel 4: e, a, ey. Optional; ey is rare.
Some languages shove an s, c, x, t, k somewhere too (some of these are probably language-specific diminutives, but a few might be phoneme drift instead) ...
"Kaylee" and its variant "Kayla" should probably not be counted (despite almost fitting the pattern) since that's a compound of "Kay", adding the additional "Leigh" name.
It goes beyond that. Three of the authors have east-asian last names.
I understand that many people from east asia have a given name in their native language and an english sounding name that they often choose themselves.
If those three authors did chose their english names, then they too fall into the same category of parents who chose a variation of Katherine.
This phenomena also occurs in the transgender community; people put a lot of thought and intention choosing their new names only to wind up surrounded by other people who also landed on the same name, often for similar reasons. There's even a whole subreddit specifically for transfeminine people who are named some variation of Lily: https://www.reddit.com/r/LilyIsTrans/
If they did indeed pick those names while traveling to the US, possibly as adults, I think they’d actually really interesting cases. They’d be choosing names later than their peers, so they could see how the name game played out for their peers. Of course, they could also be peers of the parents of the other authors.
I’ve also met some folks who had English names that phonetically sounded similar to their original names. I wonder if there’s an east Asian first name that sounds like any of the versions of Katherine.
From my anecdotal experience origin is a big factor: of adults I have known to choose a name for themselves americans overwhelmingly pick unusual or ornamented names, whereas the other group (typically asian, first language has a different set of basic sounds) pick stereotypically common and plain/short names. I don't really know anyones specific thought process on the matter though, maybe I'll have to start asking for curiosities sake.
Anecdotal, of course, but the goal can be quite different for both groups.
English people choosing English baby names often want them to be relatively unique or stand out in some way. At the very least, they don't want them to be _overly_ common.
Manny people I've talked to that have chosen a name after immigrating are kind of aiming for the opposite. They want to fit in. They already feel that they stand out, and generally try and minimize that.
There's also the fact that for some groups, they're choosing the name at a time when they may not be very familiar with English names or culture, and may not have much in the way of local resources they can or feel comfortable with drawing on, so the main indication they have that they haven't chosen some absurd name is "hey, lots of people here are named that".
Not sure it's still the same scenario with today's far more connected world, but even 20 years ago you could guess with some accuracy that someone was east-Asian from their "English" name being ~50 years out of date, popularity wise.
> For instance, a parent might anticipate the name “Kate” would be a pleasantly traditional yet unique name with only moderate popularity. They would be wrong [6].
Reference 6 is the paper.