DeclareBibliographyOption{myname}{edefsomename{#1}}

! You can't use `macro parameter character #' in horizontal mode.
@removeelement #1#2#3->def reserved@a ##1,#1,##
                                                  2reserved@a {##1,##2rese...

l.59 ProcessOptionsrelax

edefx{M{"u}ller}
edefy{M"uller}
ifdefstrequal{x}{y}{TRUE}{FALSE}

M{"u}ller
M"uller
Müller

documentclass{article}
usepackage[T1]{fontenc}
usepackage[utf8]{inputenc}
usepackage{etoolbox}

makeatletter
defstripbraces#1#2{%
  begingroup
  defIeC##1{##1}%
  protected@edef@tempa{#1}%
  gdef@gtempa{}%
  expandafter@stripbraces@tempa@nil
  endgroup
  let#2@gtempa
}
def@stripbraces#1{%
  ifx#1@nilelse
    expandaftergdefexpandafter@gtempaexpandafter{@gtempa#1}%
    expandafter@stripbraces
  fi
}

makeatother

begin{document}

stripbraces{M"uller}{x}
stripbraces{M{"u}ller}{y}
stripbraces{Müller}{z}

ifdefstrequal{x}{y}{TRUE}{FALSE}

ifdefstrequal{x}{z}{TRUE}{FALSE}

ifdefstrequal{y}{z}{TRUE}{FALSE}

stripbraces{Øre}{x}
stripbraces{{O}re}{y}
stripbraces{O re}{z}

ifdefstrequal{x}{y}{TRUE}{FALSE}

ifdefstrequal{x}{z}{TRUE}{FALSE}

ifdefstrequal{y}{z}{TRUE}{FALSE}

stripbraces{Gauß}{x}
stripbraces{Gau{ss}}{y}
stripbraces{Gauss}{z}

ifdefstrequal{x}{y}{TRUE}{FALSE}

ifdefstrequal{x}{z}{TRUE}{FALSE}

ifdefstrequal{y}{z}{TRUE}{FALSE}

end{document}

newcommandtestuni{}
DeclareBibliographyOption[boolean]{test-unicode}[false]{
ifstrequal{#1}{𐎑𓀀ຢഓæçøûüŧũǻΦ}{renewcommandtestuni{𐎑𓀀ຢഓæçøûüŧũǻΦ has matched}}{renewcommandtestuni{𐎑𓀀ຢഓæçøûüŧũǻΦ has not matched}}
}

test-unicode=𐎑𓀀ຢഓæçøûüŧũǻΦ,

Result of textbackslash testuni: {funicode testuni}.

test-unicode=𐎑𓀀ຢഓæçѾѬøûüŧũǻΦ,