Hello Michael,
In Function[x, body], the variable 'x' is the first 'argument' and the expression 'body' is the second 'argument'.
The variable 'x' is effectively a 'local' (Module) variable inside Function and hence, as shown below, the function evaluation does not depend upon its name.
IIn[1]:= f = Function[x, x^2];
In[2]:= g = Function[a, a^2];
In[3]:= f[5]
Out[3]= 25
In[4]:= g[5]
Out[4]= 25
In[5]:= f[x]
Out[5]= x^2
In[6]:= g[x]
Out[6]= x^2
Also, technically, Function has the attribute HoldAll:
In[7]:= Attributes[Function]
Out[7]= {HoldAll, Protected}
In practice, this means that the second argument 'body' is not evaluated by Function, so Evaluate is required below (since 'body' is defined outside Function).
In[8]:= body = x^2;
In[9]:= Function[x, body][5] (*incorrect*)
Out[9]= x^2
In[10]:= Function[x, Evaluate[body]][5] (*correct*)
Out[10]= 25
Hope this helps.