Another way:

BracketedVector[letter_String, n_Integer] := 
 ToExpression[
  StringJoin["Array[HoldForm[", letter, "],{", ToString[n], "}]"]]

But if all you want is an inert vector, why not use strings directly, instead of symbols? For example

BracketedVector2[letter_String, n_Integer] := Array[letter, {n}]

Try the following code: Notice that I added the underscores, replaced the comma with a semicolon, and the return is not required.

ClearAll[BracketedVector]
BracketedVector[letter_String,n_]:=Module[{i,name},
 name=Symbol[letter];
 Table[name[i],{i,n}]
]

ClearAll is just needed to be sure you don't have multiple definitions of your BracketedVector function:

BracketedVector[letter_String,n_Integer] := .......

will not automatically overwrite

BracketedVector[letter_,n_] := ....

So you are left with two definitions! It will first check the most specific one (is your first argument a string, and the second an integer?), if that one doesn't match it will try the second definition.

In your case you don't need to clear letter. This is part of the pattern (by using an underscore) and is therefore local, In fact you really don't need the module at all:

BracketedVector[letter_, n_] := Table[Symbol[letter][i], {i, n}]

will just work fine, and gives identical results. Module is just needed if you want some local variables, here you don't need any. i,n,letter are all 'local' in some sense: letter and n are local because they are part of SetDelayed, and i is local because it is used in Table. To make your code even more easy to read, you can ditch Table and it's variable i altogether, and use Array:

BracketedVector[letter_, n_] := Array[Symbol[letter], n]

again, same output, incredibly easy to read, no other variables, and better performance!

Thanks for the replies, I'll try that. Sorry, I had underscores after the module arguments, but there were automatically erased by the posted in window. The comma after name=Symbol[letter] was my typo.

Why is it necessary to clear BracketedVector? That is a module name, not a variable. Is it necessary to do before each invocationof the module? As regards Return, I always use it, since it self documents what is being returned - exactly as in C.