Utiliszing a simple logging of IP addresses and interface used via /etc/ppp/ppp.linkup, it has been revealed that in contrary to the manpage ppp(8), the variable INTERFACE is not substituted as MYADDR, MYADDR6, HISADDR, HISADDR6 is.

This following simple background statement shows the problem:

!bg     /usr/bin/logger -s -t ppp -p user.warning "Link up (INTERFACE): my-isp-name inet: MYADDR  inet6: MYADDR6"

While MYADDR and MYADDR6 are substituted by the appropriate IPv4/IPv6 addresses, INTERFACE stays as it is but I would expect /dev/tun0 or tun0.