This depends on the program reading the configuration files. The usual convention is that configuration files must end in
.conf, but nothing enforces this. For example
modprobe doesn't parse configuration files with names not ending in
'.alias' or '.conf'. modprobe used to warn about these files.
(And before that it used them without any warning at all.) Or
Moreover, the configuration mechanism in Debian has changed. All
configurations in sites-enabled and conf-enabled need a ".conf" suffix now.
Some programs use
run-parts, which again has its own conventions (even multiple ones) for the names of allowed files (see its manual). Others may also implement their custom conventions. Be careful and read the documentation to avoid surprises.