I don't do dialup anymore. But, looking at my old PPP setup (I'm
surprised I still have it), 'dns-addr' is assigned in /etc/ppp/options.
Yeah, there's a lot going on in ppp systems.
I was slightly surprised how the old scripts I used for dialup over 20 years (and a different country) ago were still used for LTE modem connections, complete with an even larger set of AT commands to control the device. I still think of AT commands as "Hayes" commands, even though Hayes themselves haven't existed this century. (Dennis Hayes still exists personally, as far as I know, as does his business partner Dale Heatherington - who retired at age 37 in the mid 80s, and seems to have had a great time since then.)
(there's a github link to the source in there for folks who might build their own)
Stewart