Oooh, I like this question. And I have data to contribute!
This data set is from the Israel Genealogy Research Association's "All Israel Database" (http://genealogy.org.il/AID/index.php) which, as of August 2015, covers over 576,000 records that were collected in, or chiefly about, the land of Israel in its Ottoman period, British Mandate period, and modern period. Because of privacy laws, almost none of the records is newer than 1965, i.e. fifty years ago. Most of the records in the database come from the late nineteenth and early 20th centuries, from a variety of libraries and sources. They cover all religions and ethnic groups in the land, but practically speaking, at the moment they are hugely over-represented with mostly-Jewish source material -- or perhaps a more accurate description would be source material that was far more likely to feature the names of Jews, such as the lists of illegal immigration during the Mandate period, i.e. the Atlit Database (מסד נתונים עתלית). More content is going online all the time, including content explicitly from other ethnic and religious groups; one of the newest big databases is for baptisms and burials at Christ Church in Jerusalem, for example.
Finally, some of the original material was written in Hebrew and some in English, so a standardized transliteration system was put together to handle bilingual indexing in a consistent way. For example, the name "רחל" usually used to get transliterated as "Rachel" (English) or "Ruchel" (Yiddish), but they chose to transliterate it using standardized modern spelling as "Rahel". Similarly, Moses gets transliterated as Moshe, Abraham as Avraham, etc.
So, with that long but necessary preamble out of the way, here are the top fifty English language given names in the 570,000+ records of the database so far, either spelled exactly as they were in their original English sources or else transliterated in a standardized way from Hebrew sources. The numbers in parentheses are the actual count of how many times they appear in the database, not a percentage, as a single record can hold multiple names (i.e. parents and child), but the Power Law pattern is pretty clear:
01. Moshe (32,913)
02. Avraham (28,445)
03. Yosef (25,225)
04. Yaakov (23,921)
05. Yitzhak (22,996)
06. David (19,704)
07. Haim (17,884)
08. Shlomo (14,509)
09. Shmuel (14,063)
10. Sara (12,046)
11. Mordekhai (11,795)
12. Tzvi (11,408)
13. Israel (11,176)
14. Aharon (10,240)
15. Yehuda (10,088)
16. Rahel (9,845)
17. Esther (9,738)
18. Meir (9,715)
19. Miriam (8,866)
20. Hana (8,559)
21. Eliahu (8,446)
22. Arie (7,882)
23. Rivka (7,704)
24. Lea (6,984)
25. Eliezer (6,814)
26. Shimon (6,408)
27. Dov (6,200)
28. Zeev (5,760)
29. Shalom (5,720)
30. Haya (5,456)
31. Yehoshua (5,060)
32. Menahem (5,021)
33. Benyamin (4,819)
34. Shushana (4,727)
35. Barukh (4,051)
36. Malka (3,803)
37. Tzipora (3,721)
38. Leib (3,641)
39. Pinhas (3,576)
40. Efraim (3,488)
41. Mikhael (3,400)
42. Devora (3,300)
43. Rafael (3,275)
44. Natan (3,260)
45. Simha (3,251)
46. Reuven (3,160)
47. Yehudit (3,122)
48. Nisim (2,971)
49. Zalman (2,945)
50. Nahum (2,893)
And here's the top fifty Hebrew language given names in the database so far, either spelled exactly as they were in their original Hebrew sources or else transliterated in a standardized way from English sources:
01. (משה (34,212
02. (אברהם (30,718
03. (יוסף (28,334
04. (יעקב (27,020
05. (יצחק (25,530
06. (דוד (20,057
07. (חיים (19,621
08. (שלמה (15,004
09. (שמואל (14,940
10. (שרה (13,744
11. (צבי (13,655
12. (מרדכי (13,567
13. (רחל (12,069
14. (ישראל (11,823
15. (אסתר (10,785
16. (מאיר (10,325
17. (חנה (10,255
18. (יהודה (9,895
19. (מרים (9,475
20. (אליהו (8,879
21. (רבקה (8,583
22. (אריה (8,382
23. (אהרן (8,045
24. (לאה (7,882
25. (אליעזר (7,256
26. (שמעון (6,637
27. (חיה (6,505
28. (זאב (6,296
29. (שלום (5,891
30. (מנחם (5,772
31. (דב (5,620
32. (שושנה (5,522
33. (בנימין (5,388
34. (יהושע (5,158
35. (ברוך (4,958
36. (מיכאל (4,139
37. (מלכה (4,051
38. (פנחס (4,034
39. (צפורה (4,032
40. (דבורה (3,964
41. (שמחה (3,698
42. (נתן (3,652
43. (אפרים (3,616
44. (ציון (3,615
45. (יהודית (3,569
46. (רפאל (3,475
47. (ראובן (3,419
48. (בן (3,180
49. (נחום (3,175
50. (אהרון (3,078
If you can read Hebrew a little, you'll notice that the two lists do not correspond exactly! For example, in English sources, Rahel is #16, while in Hebrew, it's #13. And some of the names start to diverge more and more because of genuine spelling variants, as the lists go on; for example, on the Hebrew list, #23 and #50 are both acceptable ways to spell the name Aaron/Aharon, which is way up at #14 on the English list.
So yes, Power Laws certainly seem to be in effect here too, with certain given names seen far more frequently than others.
However, your comment makes the assumption that certain names came to prominence in England in your initial data set because first-born sons were named for their fathers, daughters for mothers, etc. This data set would break that assumption, because Ashkenazi Jews (from Eastern Europe) do not name for living relatives, but rather for a recently deceased close relative, such as grandparent or great-grandparent. And Sephardic Jews (from Iberia originally, dispersed mainly to the Mediterranean and Caribbean after 1391/1492) have another tradition entirely, where they name a first-born son for a paternal grandfather, first-born daughter for a grandmother, repeat with the maternal side, and only then start adding in new and unique names. Most of the surnames in the IGRA database tend to heavily favor traditionally Ashkenazi surnames (Friedman, Katz, Goldberg, Shapira/Shapiro, etc.) so I would assume their given name naming patterns probably predominate in the data set too.
Also potentially impacting the name re-use: gender! Traditionally, Jewish males needed a Hebrew/Biblical name, so they could be called up to read to the congregation from the Torah (Old Testament), but women were not called up to the Torah to read and lead prayers and so could be named for a Biblical figure or just a common vernacular language name, in whatever country they lived. So you'll notice the relatively few female given names that managed to crack this Top 50 list were Biblical names, but there's a lot more diversity in the womens' names, so the Power Law is weaker, more diffuse. In fact, #68 on the list would be "Frida" and #88 would be "Roza" -- neither name Biblical, obviously, but more just a reflection of common names for women in the early 20th century. You even get hundreds of Charlotte's and Margaret's as the list goes on, too, and eventually it stops looking like what you'd think of as a traditionally Israeli or Jewish name list and just becomes more reflective of the fashionable female names of the time period.
Finally, I'd be remiss if I didn't point out that the All Israel Database is entirely free to use and search, although you do need to sign up and make a user account first. It's quick and free, though. They have an amazing amount of other content online, including research guides and webinars, and IMHO it's definitely worth becoming an annual member to help support their work: http://genealogy.org.il/