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Do you really not want to just have a function of two variables, such as the following?

sage: def f(i,x):                   
....:     return x^(-i)

sage: f(2,2)
1/4
sage: f(3,2)
1/8

I think there is some problem with making a list of lambda functions, but you could use the idea of a "factory" -- a function that returns another function:

sage: def named_function_factory(i):
....:     def f(x):
....:         return x^(-i)
....:     return f
....: 
sage: functionlist = [named_function_factory(i) for i in range(10)]
sage: functionlist[2](2)
1/4
sage: functionlist[3](2)
1/8

But note that this is really not so different from just using a function of two variables, i and x, so maybe I still haven't answered your question. But I also don't see an appreciable difference between typing "functionnamei(x)" and "functionname[i](x)" or "functionname(i,x)" for that matter. These are of course quite different in terms of their data types, but is that so significant here?