How to create a list of variable names to some function of that variable

Question

For example, for a single variable I can write

Print[Unevaluated[a], "=", f[a]]

But if I try the next thing I'd think of doing, assuming I want a list, it doesn't work (as intended):

Print[Unevaluated[#], "=", f[#]] & /@ {a, b, c}

This will print the actual value of a, instead of "a" itself (i.e. the variable name.) Any thoughts how I can achieve this?

-- Edit:

To be perfectly clear, I want something like:

{{"a", f[a]}, {"b", f[b]}, ...}

as the output. It tentatively seems to me that this just simply isn't possible (without putting a Hold or similar on every single thing in the list ...), but I hope I'm wrong.

-- Another edit:

Thanks for the comments; I've almost been able to do what I need. Here's the essential code:

{ SymbolName@Unevaluated[#] & /@ Unevaluated /@ Unevaluated@#1,
  Distribute[f[#1, #2], List]} & @@ 
  Unevaluated /@ Unevaluated@{{x, b, c}, {x, y}}

with output

{{x,b,c},{f(2,2),f(2,y),f(b,2),f(b,y),f(c,2),f(c,y)}}

Note that I'm only able to print "{x, b, c}" here. I actually would like a tree; i.e.,

{{x,{x,y}},{b,{x,y},{c,{x,y}}, {f(...), ...}

or something that is equivalent in letting my match the input to the output ..., any thoughts? I'm trying this myself but I keep getting stuck with how Unevaluated treats parameters ... (i.e. it's not listable; and Distribute seems to require that, in order to work in the expected way...)

(I should note, the only reason I want that tree form is because getting the exact form I asked for initially within the confines of the Distribute and so on seems harder (I couldn't work it out ...).) I don't actually care how it comes out, as long as I can Partition or whatever to get the appropriate structure.

-- Final edit:

Just incase anyone is interested, here is what I finally went with; it may not be amazingly elegant, but it's sufficient for what I needed. Note that it's actually neccessary to duplicate the expressions into the Unevaluated calls (afaik).

fMap = Flatten[Outer[f[#1, #2], A, B, 1]];
n1 = SymbolName@Unevaluated[#] & /@ 
   Unevaluated /@ Unevaluated[{x, b, c, d}];
n2 = SymbolName@Unevaluated[#] & /@ 
   Unevaluated /@ Unevaluated[{x, y, z}];

I can then create the listing I wanted via

Grid[{
    grid1 = 
     Flatten@Insert[n1, ConstantArray["", Length@n2 - 1], 
       Table[{i + 1}, {i, Range[Length@n1]}]],
    grid2 = Flatten@ConstantArray[n2, Length@n1],
    fMap
    }\[Transpose], Frame -> All];

Answer 1

Print[{ToString@#, f @@ #}] & /@ HoldForm /@ Unevaluated@{a, b, c}
(* or *)
Print[{ToString@#, f @@ #}] & /@ Defer/@ Unevaluated@{a, b, c}

to get

{"a", f[1]}
{"b", f[2]}
{"c", f[3]}

printed. Remove Print, i.e. use {ToString@#, f @@ #} & /@ HoldForm /@ Unevaluated@{a, b, c} to get {{"a", f[1]}, {"b", f[2]}, {"c", f[3]}}.

To get {"a", f[a]} {"b", f[a]} {"c", f[a]}, change f@@# to f@#.

Answer 2

Literally following what you've suggested you need as output:

{{"a", f[a]}, {"b", f[b]}, ...}

i.e. A list containing the string form name of a variable and the application of function f to that variable we get:

{SymbolName@#, HoldForm@f[#]} & /@ {a, b, c}

{{"a", f[a]}, {"b", f[b]}, {"c", f[c]}}

I hope this was what you wanted.