Changed "name" field:
from:
"name": "comwrap/module-elasticsuite-blog-search"
to:
"name": "comwrap/comwrap_elasticsuiteblog"

The reason:

After appending to composer.json:
    "repositories": {
...
        "comwrap-comwrap_elasticsuiteblog": {
            "url": "https://github.com/comwrap/Comwrap_ElasticsuiteBlog",
            "type":"git"
        }
...

Allowed:

composer require comwrap/comwrap_elasticsuiteblog

Initial status:

provided with issue:

Your requirements could not be resolved to an installable set of packages.

  Problem 1
    - The requested package comwrap/comwrap_elasticsuiteblog could not be found in any version, there may be a typo in the package name.

Potential causes:
 - A typo in the package name
 - The package is not available in a stable-enough version according to your minimum-stability setting
   see <https://getcomposer.org/doc/04-schema.md#minimum-stability> for more details.
 - It's a private package and you forgot to add a custom repository to find it

Read <https://getcomposer.org/doc/articles/troubleshooting.md> for further common problems.