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!

OK, I tried David's and Sander's suggestions, and one does the trick:

      Clear[letter]   inside the module

ClearAll[BracketedVector] is not needed and in fact "deinitializes" the module name. So the new code is a one liner:

BracketedVector[letter_,n_]:=Module[{i}, Clear[letter]; Return[Table[Symbol[letter][i],{i,n}]]];

I was able to redo my 6 matrix/vector symbolic constructors (vector, rectangular matrix, square matrix, symmetric matrix, bisymmetric matrix, and entry debracketer) and all test fine. Thanks again!

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}]
]