You are correct to use get_header() function. However, as per [documentation][1] you should pass the name of the custom header in the specific format - only the part that comes between 'header-' and '.php'. E.g. for the custom header in the file:
header-custom.php
you should use:
get_header('custom');
But that's not all. It is important to remember that the custom header file should be placed in 1 or 2 specific directories, depending on whether you're working on parent or child theme:
1. Parent theme: you should place it either in the same directory as the page template or the 'root' theme directory (specifically the same directory where your style.css is)
2. Child theme: you have to place it in the 'root' child theme directory
get_header() function calls [locate_template() function][2], which searches for the custom header file in those 2 directories. If it doesn't find the file, it defaults to 'header.php'.
[1]:
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[2]:
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