There is no “standard” command which provides the behaviour you’re after. However, on Debian and derivatives, you can use start-stop-daemon’s --stop action with the --retry option:
start-stop-daemon --stop --oknodo --retry 15 -n daemontokill
will send SIGTERM to all processes named daemontokill, wait up to 15s for them to stop, then send SIGKILL to all remaining processes (from the initial selection), and wait another 15s for them to die. It will exit with status 0 if there was nothing to kill or all the processes stopped, 2 if some processes were still around after the second timeout.
There are a number of options to match processes in various ways, see the documentation (linked above) for details. You can also provide a more detailed schedule with varying timeouts.
start-stop-daemon is part of the dpkg package so it’s always available on Debian systems (and derivatives). Some non-.deb distributions make the package available too; for example, openSUSE Leap 42 has it. It’s quite straightforward to build on other platforms:
git clone https://salsa.debian.org/dpkg-team/dpkg.git
cd dpkg
autoreconf -fi && ./configure && make
You’ll need autoconf, automake, libtool, gettext. Once the build is finished you’ll find start-stop-daemon in the utils directory.