For openSUSE Slowroll run the following as root:
zypper addrepo https://download.opensuse.org/repositories/X11:COSMIC:Next/openSUSE_Slowroll/X11:COSMIC:Next.repo
zypper refresh
zypper install cosmic-notifications
For openSUSE Factory run the following as root:
zypper addrepo https://download.opensuse.org/repositories/X11:COSMIC:Next/openSUSE_Factory/X11:COSMIC:Next.repo
zypper refresh
zypper install cosmic-notifications
For 15.6 run the following as root:
zypper addrepo https://download.opensuse.org/repositories/X11:COSMIC:Next/15.6/X11:COSMIC:Next.repo
zypper refresh
zypper install cosmic-notifications