Macro defining macro defining global macro (similar to `\author` or `\title` fields)

The definition of \DefineField has a superfluous space in \gdef\csname @#1 \endcsname{##1}%, it should be

\def\DefineField#1{%
  \expandafter\edef\csname #1\endcsname##1{%
    \gdef\csname @#1\endcsname{##1}%
  }%
}

With the space you would define the command \@Alice␣ (where ␣ represents a space) as can be verified by checking \@Alice␣'s definition with

\expandafter\show\csname @Alice \endcsname

If we want to define \@Alice we need to get rid of the space.

---

Note that the use of \edef in \DefineField can have unintended consequences, so you may want to consider going for the solution presented in Martin Scharrer's answer or egreg's answer.

I would not use \edef here but work with a second \expandafter.

The main problem here is that you have a space between #1 and \endcsname, so you actually define \@Alice<space>, which is possible with \csname.

Correct code is:

\def\DefineField#1{%
    \expandafter\def\csname #1\endcsname##1{%
        \expandafter\gdef\csname @#1\endcsname{##1}%
    }%
}

You're defining \csname @Alice \endcsname which results in a control sequence token having a trailing space in its name. The space after \csname doesn't find its way during tokenization, because it follows a control word, but the space between #1 and \endcsname will not be removed.

Your usage of \edef is quite problematic as well: if you mistakenly use \DefineField{Alice} twice,

\DefineField{Alice}
\Alice{My name is Alice}
\show\Alice

\DefineField{Alice}
\show\Alice

you'll get

> \Alice=macro:
#1->\gdef \@Alice {#1}.

> \Alice=macro:
#1->\gdef My name is Alice{#1}.

This can be cured by checking first if \Alice is defined:

\def\DefineField#1{%
  \@ifundefined{#1}
    {% go on, it's undefined
      \expandafter\edef\csname #1\endcsname##1{%
        \gdef\csname @#1\endcsname{##1}%
      }%
    }
    {% ignore the redefinition
      \PackageWarning{andywiecko}{%
        \expandafter\noexpand\csname #1\endcsname already defined%
      }%
    }%
}

A simpler approach with xparse and expl3:

\documentclass{article}
\usepackage{xparse}

\ExplSyntaxOn

\NewDocumentCommand{\DefineField}{m}
 {
  \cs_new_protected:cpn { #1 } ##1
   {
    \cs_new_protected:cpn { @#1 } { ##1 } % or `\cs_new:cpn
   }
 }

\ExplSyntaxOff

\DefineField{Alice}
\Alice{My name is Alice}

\expandafter\show\csname @Alice\endcsname

This will produce a standard error if \DefineField{Alice} is used twice or if you try doing \DefineField{box}; the code will show

> \@Alice=\protected\long macro:
->My name is Alice.

You may want to use \cs_new:cpn in the second instance, depending on what expansion context you will use the \@Alice macro.

---

A more proper expl3 interface, where instead of defining \@foo macros you do \UseField{foo} when needed. A way to override already existing fields is provided.

\documentclass{article}
\usepackage{xparse}

\ExplSyntaxOn

\prop_new:N \g_andywiecko_fields_prop
\cs_new:Nn \andywiecko_define_field:nn
 {
  \prop_gput:Nnn \g_andywiecko_fields_prop { #1 } { #2 }
 }

\NewDocumentCommand{\DefineField}{sm}
 {
  \cs_set_protected:Nn \__andywiecko:n
   {
    \andywiecko_define_field:nn { #2 } { ##1 }
   }
  \IfBooleanTF { #1 }
   {% override an existing definition
    \cs_gset_eq:cN { #2 } \__andywiecko:n
   }
   {% new field
    \cs_new_eq:cN { #2 } \__andywiecko:n
   }
 }

\NewExpandableDocumentCommand{\UseField}{m}
 {
  \prop_item:Nn \g_andywiecko_fields_prop { #1 }
 }

\ExplSyntaxOff

\DefineField{author} % gives error

\DefineField*{author} % no error, use new interface

\DefineField{Alice}
\Alice{My name is Alice}

\DefineField{Alice} % gives error