user11333: There is a tutorial in the Arduino website on how to create a library. The tutorial gives the following codes for the header:
class Morse
{
  public:
    Morse(int pin);
    void dot();
    void dash();
  private:
    int _pin;
};

My questions are:

What is the purpose of this line: Morse(int pin);
If any, what is the name of this line?


user6936: Morse(int pin);

is the constructor for the class, Morse.
The name of this line, and all of the other lines between the curly braces{ and } are declarations of the members of the class Morse.
So, the line 
Morse(int pin);

is the declaration of the constructor, to answer both of your questions in one line.
Constructors are required pieces of code for Object Oriented Programming. When the constructor is called, it creates an object which is an instance of the class Morse. In this constructor is where all of the initialisation of the oblject goes. In the case of Morse it just initialises pin, which is specified in the parameter pin, by setting it to be an OUTPUT.
It is declared here, as a "signpost" if you will, for other parts of the code to know that it exists and is available to be called.

user368: 

What is the purpose of this line: Morse(int pin);


It is the method that is called when you create an object of class Morse when only passing a single int:
Morse somemorse(1);



If any, what is the name of this line?


It has multiple names, depending on what aspect you care about:

It is a constructor for the class Morse.
It is a forward declaration for the method Morse::Morse(int).


11333: <p>There is a tutorial in the Arduino website on how to create a library. The tutorial gives the following codes for the header:</p>

<pre><code>class Morse
{
  public:
    Morse(int pin);
    void dot();
    void dash();
  private:
    int _pin;
};
</code></pre>

<p>My questions are:</p>

<ol>
<li>What is the purpose of this line: <code>Morse(int pin);</code></li>
<li>If any, what is the name of this line?</li>
</ol>
 6936: <pre><code>Morse(int pin);
</code></pre>

<p>is the <strong>constructor</strong> for the class, <code>Morse</code>.</p>

<p>The name of this line, and all of the other lines between the curly braces<code>{</code> and <code>}</code> are <strong>declarations</strong> of the members of the class <code>Morse</code>.</p>

<p>So, the line </p>

<pre><code>Morse(int pin);
</code></pre>

<p>is the <em>declaration</em> of the <em>constructor</em>, to answer both of your questions in one line.</p>

<p>Constructors are required pieces of code for Object Oriented Programming. When the constructor is called, it creates an object which is an instance of the class <code>Morse</code>. In this constructor is where all of the initialisation of the oblject goes. In the case of <code>Morse</code> it just initialises pin, which is specified in the parameter <code>pin</code>, by setting it to be an <code>OUTPUT</code>.</p>

<p>It is declared here, as a "signpost" if you will, for other parts of the code to know that it exists and is available to be called.</p>
 368: <blockquote>
  <ol>
  <li>What is the purpose of this line: <code>Morse(int pin);</code></li>
  </ol>
</blockquote>

<p>It is the method that is called when you create an object of class <code>Morse</code> when only passing a single <code>int</code>:</p>

<pre><code>Morse somemorse(1);
</code></pre>

<blockquote>
  <ol start="2">
  <li>If any, what is the name of this line?</li>
  </ol>
</blockquote>

<p>It has multiple names, depending on what aspect you care about:</p>

<ul>
<li>It is a <strong>constructor</strong> for the class <code>Morse</code>.</li>
<li>It is a <strong>forward declaration</strong> for the method <code>Morse::Morse(int)</code>.</li>
</ul>
