Choice of Name

How to deal with a Hebrew personal name that can be read in more than one way? For example yod-sin-resh-alef-lamed-he    according to the list of personal names  in Even-Shoshan could be both "Yesar'elah" and "Yisre'elah". The cataloger  was  within  his-her rights   to   make   the  heading  provisional  and   give   both possibilities.  The choice of which one  to make the  ref  perhaps reflects an anti-feminist bias, but  I  it's "wrong" from  a  cataloging  point  of  view.

ID:NAFL85274689    ST:p    EL:n   STH:c    MS:c   UIP:a    TD:19870212061202
KRC:a    NMU:a    CRC:c   UPN:a   SBU:a   SBC:a   DID:n    DF:12-11-86
RFE:a CSC:   SRU:b   SRT:n   SRN:n   TSS:    TGA:?   ROM:?   MOD:  LCT:
VST:d 02-13-87                      Other Versions: earlier
040    DLC$cDLC
100 10 Hanig'al, Yesar'elah.
400 10 Hanig'al, Yisre'elah
400 10 Hanig'al, Yisra'elah
667    Uncertain whether romanization of forename is Yesar'elah [m] or Yisre'elah [f].
670    Goldsh.tain, Y. Ben Tsiyon le-Tsiyonut, c1979- :$bv. 1, t.p. verso (Yesar'elah Hanig'al)

The same stands for the following [m]: Alon and Elon [alef-lamed-vav-nun], Ayalon and Elon [alef-yod-lamed-vav-nun], El'uzi and El'uzai, Oren and Aran [alef-resh-nun], Bani, Buni, Benai and Beni [bet-nun-yod], Hadar and Heder, .Hagai and .Hagi, .Hanan and .Hinan, Yig'al and Yiga'el, Yeru.ham and Yero.ham, Mikhayahu and Mikhaihu, Sali and Salai, 'Eden and 'Idan, Pal.ti and Pil.tai, Tsa.her nad Tso.har, .Kora.h and .Karea.h, Rame and Rami, Ran and Ron [resh-nun], Shelomi, Shalmai and Salmai, Shemah and Shumah, Shema' and Shama', Talmai and Talmi, or the following [f]: Oholah and Ohelah, Alonah and Elonah, Ornah and Ernah, Asherit and Oshrit, Bare.ket and Bar.kat, .Hanah and .Hinah, .Hanit anf .Hinit, Ye'elah and Ya'alah, Le.viyah and Loyah [lamed-vav-yod-he], Segulah and Siglah, 'Eliyah and 'Aliyah, 'Arevah and 'Aravah, Tsivyah and Tseviyah,  Ramah and Remah

It is much rarer to find combinations that can form either male or female names: Itai [m] or Eti [f], Levana [m&f] and Livnah [f], Na'eh [m] and Na'ah [f] [nun-alef-he], Na.veh [m] and Na.vah [f] [nun-alef-vav-he], .Kelayah [m] and .Kalyah [f], Rinah [m&f]and Ronah [f]

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How should the name of the author of Unter shtile himeln (Warsaw, 1921) who wrote in Yiddish under the pseudonym
Der Hasid (real name: Teomim, David) be established?   in Hebrew (Hasid) or Yiddish (Hosed)?

Unless other rules apply, an author's name should be established in the language of the work in which it appears--
cf. rule 22.1B.   In this case, that's Yiddish.  A reference from another possible romanization of the name, in this case a Hebrew one, is always allowed.

ID:NAFR9932426     ST:p    EL:n   STH:a    MS:n   UIP:a    TD:19991019013733
KRC:a    NMU:a    CRC:c   UPN:a   SBU:a   SBC:a   DID:n    DF:10-15-99
RFE:a CSC:c  SRU:b   SRT:n   SRN:n   TSS:n   TGA:?   ROM:?   MOD:  LCT:
VST:d 10-21-99
010    nr 99032426
040    CSt-HC$beng$cCSt-HC
100 0  .Hosed,$dd. 1943
400 0  .Hasid,$dd. 1943
400 1  Te'omim, Da.vid,$dd. 1943
400 1  Thumim, David,$dd. 1943
670    Un.ter sh.tile himeln, 1921:$bt.p. (Der .Hosed)
670    Le.ksi.kon fun der nayer Yidisher li.tera.tur, 1956-1981$b(Te'omim, Da.vid; d. Jan. 1943)
670    Otsar biduye ha-shem, 1967:$bp. 60 (Thumim, David)
675    Ency. Judaica, c1972.

[shouldn't Te'omim be a 500? there's no independent NAR for the real name. NjPG's NAR is for another person]

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What should be the entry element of the name Yits.ha.k b.R. Mena.hem Monish ha-Kohen, zal, mi-Druis.k?

The forename "Manish" or "Monish" often goes with "Menahem," so it would be better to treat it as a forename here.  Making a ref from it as a surname is fine.

Whether "ha-Kohen" should be treated as a surname or a $c is a trickier question.  The practice is to treat it as a $c for a
pre-20th-century author, unless there's evidence the other way.  In this case, there IS evidence, namely the treatment in Bet 'eked.  Bet 'eked carries a lot of authority, since it's a reference source in the author's language of activity, so it's recommended to adopt its view of the surname (and entry-element) status here.

ID:NAFR9932301     ST:p    EL:n   STH:a    MS:n   UIP:a    TD:19991019013731 KRC:a    NMU:a    CRC:c   UPN:a   SBU:a   SBC:a   DID:n    DF:10-14-99       RFE:a CSC:c  SRU:b   SRT:n   SRN:n   TSS:n   TGA:?   ROM:?   MOD:  LCT:      VST:d 10-21-99
010    nr 99032301
040    CSt-HCbengcCSt-HC
100 1  Hakohen, Yits.ha.k ben Mena.hem Monish
400 0  Yits.ha.k ben Mena.hem Monish,$cha-Kohen, mi-Druis.k
400 1  Monish, Yits.ha.k ben Mena.hem,$cha-Kohen
400 0  Isaak Monish
670    Sefer Li.ku.te Yits.ha.k, 1891:$bt.p. (Yits.ha.k b.R. Mena.hem Monish ha-Kohen, zal, mi-Druis.k) t.p. verso ( ... Isaaka Monysha [in Cyr.])
670    Bet 'e.ked sefarim, 1951-1956$b(hdg.: Hakohen, Yits.ha.k)
675    Ency. Judaica, c1972.