How should an author's name, described on the chief source by a phrase, be established?

Rule 22.11D says: "Enter a characterizing word or phrase, or a phrase naming another work by a person, in direct order. Omit an initial article. Consider such a word or phrase to be the heading for a person if that person is commonly identified by it in the chief sources of information of his or her works and in referce sources. Refer, when appropriate, from the title of the work in the form [Title], Author of." ...

"If a person is commonly identified by a real name or another name (see 22.2A), and a word or phrase characterizing that person or including the title of another work has appeared in the chief source of information of any of his or her works, refer from the word or phrase. Also, refer when appropriate, from the title of the other work in the form [Title], Author of."

RI22.11D says: "Headings referred to in this rule apply only to persons whose names are unknown (cf. 21.5C), not to persons whose names are known (cf. 21.4A)"

As a result,  the author is described by  the phrase "ha-g. ha-.k. mi-Bush.tash" in  the  chief source, whose actual name occurred elsewhere in the piece as "ha-g. R. Avraham Da.vid mi-Bu.tsh.ta.t", and for whom there is an entry in Enc. Jud., c1971,  should be established by his real name, as follows:.
 

ID:NAFL9739422     ST:p    EL:n   STH:a    MS:c   UIP:a    TD:20000121013743
KRC:a    NMU:a    CRC:c   UPN:a   SBU:a   SBC:a   DID:n    DF:04-15-97
RFE:a CSC:   SRU:b   SRT:n   SRN:n   TSS:?   TGA:?   ROM:?   MOD:  LCT:
VST:d 01-27-00                      Other Versions: earlier
010    n  97039422 $znr 95041288
040    DLC$beng$cDLC$dDLC-R
100 1  Wahrmann, Abraham David ben Asher Anschel,$dca. 1771-1840
400 0  Avraham Da.vid,$ca.b.d. di-.k..k Bi.tsha.tsh,$dca. 1771-1840
400 1  .Vahrman, Avraham Da.vid,$dca. 1771-1840
400 0  Avraham Da.vid,$cmi-Bu.tsh.ta.t,$dca. 1771-1840
400 0  G. ha-.K. mi-Bush.tash.t,$dca. 1771-1840
400 0  Ga'on ha-.Kadosh mi-Bush.tash.t,$dca. 1771-1840
400 0  Abraham David,$cof Buczacz,$dca. 1771-1840
400 0  Abraham David ben Asher,$dca. 1771-1840
400 0  Da°at .kedoshim,$dca. 1771-1840
670    Sefer Birkat Da.vid, 1994 or 1995:$borig. t.p. (mo. ha-r. R. Avraham Da.vid ... a.b.d. di-.k..k. Bi.tsha.tsh)
670    Encyc. Judaica, c1971$b(Wahrmann, Abraham David ben Asher Anschel; c. 1771-1840; Hasidic rabbi, b. Nadvornaya, Ukraine; rabbi of Jazlowce)
670    Enc. Jud., c1972:$bv. 12, col. 868 (Rabbi Abraham David of Buczacz) v.14, col. 1461 (Avraham David of Buczacz)
670    Bet °e.ked sefarim, 1951:$bv. 1, p. 176 (ha-R. Avraham Da.vid .Vahrman)
670    °Al Shu. °a. Ora.h .hayim, 1993:$bt.p. (ha-G. ha-.K. mi-Bush.tash.t, zatsal) 3rd prelim. p. (ha-g. R. Avraham Da.vid mi-Bu.tsh.ta.t)
670    Sefer Eshel Avraham, 1995 or 1996:$bt.p. (Rabenu Avraham Da.vid ... g.a.b.d. Bu.tsha.tsh; ha-Da°at .kedoshim)
670    NUC pre-56$b(Abraham David ben Asher, 1770 (ca.)-1840)