When is a symbol a Symbol? Is there an easy Mathematica way to test if an object is a symbol sort of like a SymbolQ?

I'd probably use x_Symbol in a function argument to control evaluation. Otherwise, one might do the following (thanks to @Leonid for pointing out an oversight).

If the argument is to be evaluated before testing:

SymbolQ = MatchQ[#, t_Symbol /; AtomQ[t]] &

If the argument is not to be evaluated:

SymbolQ = Function[s,
  MatchQ[Unevaluated@s, t_Symbol /; AtomQ[Unevaluated@t]], 
  HoldAllComplete];

Examples with the second definition:

SymbolQ@Plot

(*  True  *)

x = 1;
SymbolQ[x]

(*  True  *)

Clear[y];
SymbolQ@y[1]

(*  False  *)

---

Addendum

Here's what I had in mind for makeRuleRow:

ClearAll[makeRuleRow];
SetAttributes[makeRuleRow, HoldFirst];
makeRuleRow[symbol_Symbol, altname_ : "", desc_ : ""] := 
  "execute body of function";
makeRuleRow[symbol_, altname_ : "", desc_ : ""] := 
  Null /; (Message[makeRuleRow::sym, symbol, 1]; False);

makeRuleRow[123]

makeRuleRow::sym: Argument 123 at position 1 is expected to be a symbol.

(*  makeRuleRow[123]  *)

makeRuleRow[y]

(* "execute body of function"  *)

---

Addendum 2

1. You could use Replace or Switch to define name in either way below:

ClearAll[makeRuleRow];
SetAttributes[{makeRuleRow}, HoldFirst];
makeRuleRow[symbol_, altname_ : Null, desc_ : Null] := 
  Module[{name = "", prepend = ""},
   name = Replace[Unevaluated@symbol, {
      s_Symbol :> objectName[symbol]
      , s_ /; StringQ@altname :> altname
      , _ -> $Failed}
     ];
   prepend = If[StringQ[desc], desc <> " ", ""];
   {Row[{Style[prepend, desccolor], name, rule}], 
     TraditionalForm[symbol]} /; FreeQ[name, $Failed]];
makeRuleRow[symbol_, altname_ : Null, desc_ : Null] := Null /; (
    Message[makeRuleRow::args, makeRuleRow]; False);

2. Or:

ClearAll[makeRuleRow];
SetAttributes[{makeRuleRow}, HoldFirst];
makeRuleRow[symbol_, altname_ : Null, desc_ : Null] := 
  Module[{name = "", prepend = ""},
   Switch[Unevaluated@symbol
    , s_Symbol, name = objectName[symbol]
    , s_ /; StringQ@altname, name = altname
    , _, name = $Failed
    ];
   prepend = If[StringQ[desc], desc <> " ", ""];
   {Row[{Style[prepend, desccolor], name, rule}], 
     TraditionalForm[symbol]} /; FreeQ[name, $Failed]];
makeRuleRow[symbol_, altname_ : Null, desc_ : Null] := Null /; (
    Message[makeRuleRow::args, makeRuleRow]; False);

Some may prefer Switch because they know it from another language or just find it easier to read. Too many commas for me, and I find the Replace method easier.

3. There are a few ways to handle complicated argument checking. Another is to call an "internal" version which throws $Failed when there's is an error:

func[symbol_, altname_ : Null, desc_ : Null] := Module[{res},
   res = Catch[iFunc[symbol, altname, desc], func];
   res /; FreeQ[res, $Failed]
   ];
iFunc[symbol_, altname_, desc_] := Module[{ ...},
   If[error1,
    Message[func::err1, ...];
    Throw[$Failed, func]
    ];
   If[error2,
    Message[func::err2, ...];
    Throw[$Failed, func]
    ];
   ...
   res (* return result *)
   ];

4. Yet another way is to have the outer function process the arguments and call the internal function with canonicalized arguments (for example, iMakeRuleRow[name_, desc_]) or indicate an error. The internal function then can assume the arguments are valid.

I found my answer thanks to Sjoerd Smit who referenced me to the Mathematica Function Repository. And yes it is appropriately called SymbolQ which is used like the following...

xxx = 123
ResourceFunction["SymbolQ"][xxx] (* returns True *)

A little bit ugly and long but it works. But why not fix if it isn't broken? And that is what I tried to do...

SetAttributes[symbolQ, HoldAllComplete];
symbolQ = ResourceFunction["SymbolQ"][#] &;
symbolQ[xxx] (* returns False *)

However Sjord came up with a solution that looks eerily similar to mine which leaves me scratching my head, why doesn't my alias work?...

SetAttributes[symbolQ, HoldAllComplete];
symbolQ[x_] := ResourceFunction["SymbolQ"][x];
symbolQ[xxx] (* returns True *)

How about:

SymbolQ[_Symbol] = True
SymbolQ[_] = False

?