functions.php

<?php

function get_my_header() {
  
  // if is home, which is the front page
  if(is_home()) {
    
    // then get the header-home.php
    get_header('home');
    
  // else get the normal header.php  
  } else {
    
    get_header();
  }
    
}

functions2.php

<?php
function get_my_header() {

	if( !is_home() ) {
		
		global $post;
		// get category by ID
		$category = get_the_category($post->ID);
		// first category slug
		$catslug = $category[0]->slug; 
	
		// is there is a category slug call the header-$catslug.pgp
		if (isset($catslug)) {
		       get_header($catslug);
		} else {
			// else call normal header.php
		       get_header();
	    }// ends !is_home()
	
	// else call normal header
	} else {
		get_header();
	}// ends isset()
  
} // ends get_myheader function