Elegant manipulation of the variables list

I think that "elegant" should be syntax as close to the normal handling of symbols as possible.

I shall define a function, unimaginatively named bump, that has a syntax similar to Part but which allows operations on symbols by way of Unevaluated and UpSet. If you will consider other storage formats besides Hold[v1, v2, ...] e.g. Hold @ {v1, v2, ...} this might be simplified somewhat.

func_[a___, bump[lst_, idx___], b___] ^:= 
  func[a, #, b] & @ Part[List @@@ Unevaluated @@ {lst}, {1}, idx]

Examples:

varsH = Hold[U0[1], U0[2], B0, V0[1], V0[2]];

bump[varsH] = Range[5];    (* set all values *)

bump[varsH, 3] = 8;        (* reassignment to B0 *)

varsH[[3]]                 (* recall B0 *)

ToString @ bump[varsH, 3]  (* get name of B0 as String *)

bump[varsH, 3] =.          (* Unset B0 *)

bump[varsH] =.             (* Unset all *)

This works with other operations and shapes of lists too. (For consistency I think Hold @ {...} is better but I will use the original form.)

vars2 = Hold[a, b, {c1, c2}, d];

bump[vars2, 3, 1] = 5;
bump[vars2, 3, 2] = 7;
bump[vars2, 3] += 1;

List @@ vars2  (* show the result *)

{a, b, {6, 8}, d}

bump[vars2, 3] =.;
List @@ vars2

{a, b, {c1, c2}, d}

For a simpler function upon which this one is based see:

Assigning values to a list of variable names

Here's an approach similar to Simon Woods, but using Extract itself rather then following replacement rules:

 setTo[val_] := Function[var, var = val, HoldAll]
 mySymbolName = Function[var, ToString[Unevaluated[var]], HoldAll];

Which is then used as:

 a[1] = b = c = 1;
 vars = Hold[a, b, c];

 Extract[vars, 3, setTo[42]]
 Extract[vars, 3, mySymbolName]

And you can then clear the value using:

 Extract[vars, 3, Unset]

a[1] = a[2] = b = c = 1;
vars = Hold[a[1], a[2], b, c];

Assign new value to the variable (the variable can already have a value)

Extract[vars, 1, Hold] /. Hold[x_] :> (x = 20)

Unset the variable

Extract[vars, 1, Hold] /. Hold[x_?ValueQ] :> (x =.)

Get the current value of the variable

Extract[vars, 1]

Get the name of the variable as String

Extract[vars, 1, Hold] /. Hold[x_] :> ToString[Unevaluated[x]]

Unset all variables

Cases[vars, x_?ValueQ :> (x =.), 1]