LC practice is to consider expressions like "Forename1 ha-mekhuneh Forename2 Surname" as falling under the provisions of RI 22.2A, which directs us to omit the nickname in formulating the heading.

Example:
 

   ID:NAFR991698      ST:p    EL:n   STH:a    MS:n   UIP:a    TD: 19990120051620
   KRC:a    NMU:a    CRC:c   UPN:a   SBU:a   SBC:a   DID:n DF:01-15-99
   RFE:a    CSC:c    SRU:b   SRT:n   SRN:n   TSS:n   TGA:?   ROM:? MOD:
   VST:p 01-20-99
   010    nr 99001698
   040    CSt-HC$cCSt-HC
   100 1  Pineles, Hirsch Mendel ben Solomon,$d1806-1870
   400 1  Pinele's, Tsevi Mena.hem,$d1806-1870
   400 1  Pinele's, Hirsh Mendl,$d1806-1870
   400 1  Pinilish, Tsevi Mena.hem,$d1806-1870
   400 0  Tsevi Mena.hem,$d1806-1870
   400 0  Shalosh,$d1806-1870
   670    Sefer Darkah shel Torah, 1969?:$bt.p. (Tsevi Mena.hem  ha-mekhuneh Hirsh Mendl Pinilish)
   670    Ency. Judaica, c1972$b(Pineles, Hirsch Mendel ben Solomon (known as Shalosh), 1806-1970; Galician scholar and  writer)

------------------------

Another example is that of  "Eli'ezer ha-mekhun.  Lipman  beha-r.  R.   Menahem  Maneli,  zal,  mi-k.k. Zamosht."
An informal survey  reveals that  LC practice has been to resolve this as "Lipman, Eli'ezer."