Query on father of Hedwiga GERVAI

Complicated because of mother Klara's 2 husbands, both of whom changed surnames.

Klara married Salamon Gervai on 23 Dec 1897
Hedvig was born in 1903
Klara's second marriage was to Mr Deak on 28 April 1910

Mr Deak was therefore Hedvig's step father, but she occasionally used his surname.

See her marriage and death registrations

marriage https://familysearch.org/ark:/61903/3:1:S3HY-6L4Q-2R4?i=8&cc=14...

death https://www.familysearch.org/ark:/61903/3:1:3QS7-894V-QKBL?i=454

Similarly
Andor Gluck was born a son of Salamon Gervais in 1899
But when he married, he was using his step father's surname of Deak
https://www.familysearch.org/ark:/61903/3:1:S3HT-6SPS-LSL?i=6

There appear to be no papers suggesting that Andor or Hedvig were officially adopted by their step father, so their usage of his surname was just a matter of choice

CORRECTION OF PREVIOUS MESSAGE

Adoption papers for both children do exist after all.
They are under the second husband's correct Hungarian forename of Frigyes rather than an unverified Germanic alternative,
See
Reference code HU BFL - VII.176.a - 1912 - 1032
Database Notarial deeds
Title of archival unit VII.176.a - Budapest Főváros Levéltára. A jogszolgáltatás területi szervei. Stamberger Ferenc közjegyző iratai. Okiratok
Type örökbefogadási szerződés
Year 1912
Reference number 1032
Description magyar
Participant
Name Deák (Deutsch) Frigyes
Status/occupation kereskedő
Address/Location Budapest VI. Andrássy út 32.
Name Deák (Deutsch) Frigyesné, mint a kiskorú Gervai Andor és Gervai Hedvig természetes és törvényes gyámja Lazsánszky Klára
Status/occupation kereskedő neje
Address/Location Budapest VI. Andrássy út 32.
Name Gervai Andor kiskorú
Address/Location Budapest VI. Andrássy út 32.
Name Gervai Hedvig kiskorú
Address/Location Budapest VI. Andrássy út 32.

That being the case, do they now have to be shown as children of both husbands?