Removing given name in bibliography

biblatex already has a name format called labelname which does this. It also allows for disambiguation on the basis of the uniquename option if you use that. Just add this to your preamble:

DeclareNameAlias{default}{labelname}

If you don't wan't the initials in the following MWE, then leave out the uniquename=init option.

documentclass{article}
begin{filecontents}[overwrite]{jobname.bib}
@book{a,
  author = {Doe, Jane and Doe, John},
  title = {A Title},
  date = {2021}
}
@book{b,
  author = {Doe, Barry and Doe, Sheila},
  title = {Another Title},
  date = {2021}
}
@book{c,
  author = {Author, An and Writer, Another},
  title = {Yet Another Title},
  date = {2021}
}
end{filecontents}
usepackage[uniquename=init]{biblatex}
addbibresource{jobname.bib}
DeclareNameAlias{default}{labelname}
begin{document}
nocite{*}
printbibliography
end{document}

Addendum: Why does this work?

biblatex creates a special field for citations called labelname. Most often this is just the family name, but can include a given name or initial if we need to remove ambiguity. In order to print this field, we need a name format that just prints the family name. This name format is defined in biblatex.def as:

DeclareNameFormat{labelname}{%
  ifcasevalue{uniquename}%
    usebibmacro{name:family}
      {namepartfamily}
      {namepartgiven}
      {namepartprefix}
      {namepartsuffix}%
  or
    ifuseprefix
      {usebibmacro{name:given-family}
        {namepartfamily}
        {namepartgiveni}
        {namepartprefix}
        {namepartsuffixi}}
      {usebibmacro{name:given-family}
        {namepartfamily}
        {namepartgiveni}
        {namepartprefixi}
        {namepartsuffixi}}%
  or
    usebibmacro{name:given-family}
      {namepartfamily}
      {namepartgiven}
      {namepartprefix}
      {namepartsuffix}%
  fi
  usebibmacro{name:andothers}}

In this format there is logic for disambiguation. But if disambiguation isn't needed, then the macro name:family (also defined in biblatex.def) is called to print just the family name.

Now all we need to do is tell biblatex to use this format when printing names in the bibliography. The simplest and most global way to do this is to change the default way names are printed from given-family to labelname. We do this using an alias:

DeclareNameAlias{default}{labelname}

Be aware that not all bibliography styles use the default name format in the bibliography though. Some use sortname so you'd need to change that instead.