My understanding is that you want to distribute/deploy a package to multiple Debian based distributions.
In the Debian/Ubuntu world, you should not provide individual
.deb file to download and install. Instead you should provide an APT repository. (in the Fedora/Red Hat/CentOS world I would make a similar advice to provide a YUM repository). Not only does is solves issue of how to name deb file, but repository is an effective way to provide newer version of your package, including bug-fix and security updates. Creating an APT repository is beyond the purpose of this page/question, just search for "how to setup an apt repository"
Now back to your question: "package naming convention":
When you generate the package with
dpkg-buildpackage, the package will be named in a standard way. Quoting dpkg-name manpage:
A full package name consists of package_version_architecture.package-type as specified in the control file of the package.
The Debian Policy is the right place to know the syntax of the control files: name (for both Source and binary packages), version, architecture, package-type.
There is no provision to state the distribution, because this is not how the way thing goes.
If you need to compile the same version of a package for multiple distributions, you will change the
version field (in the
debian/control file). Some people use the distribution name in the version field. for example openssl:
If that's what you want to do, make sure to read debian-policy about
debian_revision in version.