The first argument to the system stored procedure [`sp_helptext`][1] is:

>`[ `**`@objname`**` = ] 'name'`  
Is the qualified or nonqualified name of a user-defined, schema-scoped object. Quotation marks are required only if a qualified object is specified. If a fully qualified name, including a database name, is provided, the database name must be the name of the current database. The object must be in the current database. name is **`nvarchar(776)`**, with no default.

In addition, the documentation for Delimited Identifiers (Database Engine) states:

>**[Using Identifiers As Parameters in SQL Server][2]**  
Many system stored procedures, functions, and DBCC statements take object names as parameters. Some of these parameters accept multipart object names, while others accept only single-part names. Whether a single-part or multipart name is expected determines how a parameter is parsed and used internally by SQL Server.
>
>**Single-part Parameter Names**  
If the parameter is a single-part identifier, the name can be specified in the following ways:
>
> * Without quotation marks or delimiters
> * Enclosed in single quotation marks
> * Enclosed in double quotation marks
> * Enclosed in brackets
>
>**Multipart Parameter Names**  
Multipart names are qualified names that include the database or schema name and also the object name. When a multipart name is used as a parameter, SQL Server requires that the complete string that makes up the multipart name be enclosed in a set of single quotation marks.

---

The first argument to `sp_helptext` accepts both single-part (nonqualified) and multipart (qualified) object names.

If the T-SQL parser interprets the item after `sp_helptext` as a **single-part name** (in accordance with the four bullet points above), the resulting name is passed as the (string type) argument value expected by the procedure.

When the parser sees it as a **multipart name**, the text is required to be surrounded with single quotation marks as stated.

The key feature of a multipart name is a `.` separator (outside any delimiters).

These examples from the question are successfully interpreted as single-part names:

- `myproc` --- single-part (without quotation marks or delimiters - bullet #1)
- `[myproc]` --- single-part (in brackets - bullet #4)
- `'myproc'` --- single-part (in single quotation marks - bullet #2)
- `'dbo.myproc'` --- **multipart** with the required single quotation marks
- `[dbo.myproc]` --- single-part (in brackets - bullet #4)

The last two examples from the question are both parsed as multipart parameter names (due to the exposed `.` separator). They produce an error because they lack the required enclosing single quotation marks:

- `dbo.myproc` --- multipart without the required single quotation marks
- `[dbo].[myproc]` --- multipart without the required single quotation marks

This extra example using double quotation marks is successful:

- `"dbo.myproc"` --- single-part (in double quotation marks - bullet point #3)

Note that it is successfully interpreted (for the procedure parameter value) as being a valid **single-part** name, but the procedure code is able to interpret the (multipart) string it receives flexibly (using [`PARSENAME`][3] and [`OBJECTID`][4]).

As a final point of interest, note that using double quotation marks here does not depend on the setting of [`QUOTED_IDENTIFIER`][5].

  [1]: https://msdn.microsoft.com/en-us/library/ms176112.aspx
  [2]: https://technet.microsoft.com/en-us/library/ms176027.aspx#Anchor_2
  [3]: https://msdn.microsoft.com/en-us/library/ms188006.aspx
  [4]: https://msdn.microsoft.com/en-us/library/ms190328.aspx
  [5]: https://msdn.microsoft.com/en-us/library/ms174393.aspx