That's getting more and more difficult. Some routers will support it, but you lose access to simultaneous dual band or some such because most of the 802.11ac chipsets aren't being manufactured in ways that lend themselves to OSS development. Linksys had that AC1200 router for a while that was great, but there was never a Tomato release for it and Linksys discontinued it pretty quickly. The AC3200 is also DD-WRT supported, but at $300, it's not for the faint of wallet.

Meanwhile, for pretty much the rest of the Linksys line, locked bootloaders have been becoming a standard. Asus is already pretty much there, and while I haven't tried to flash a Netgear router of late, they look like they're playing games with the revision numbers that they don't exactly advertise. Haven't touched a D-Link router in years, TP-Link was the first to do the whole locked bootloader crap, and the crappy routers doled out by Verizon, Comcast, Cox, Spectrum, and Altice don't even count as routers if DDNS updating is something cared about. Tenda has a handful that will support DD-WRT or Tomato, but your wi-fi signal will be hobbled because the generic drivers do the job, but don't do some of the advanced stuff that gives better performance. The FSF only lists their sole certified router as unavailable, which is unsurprising because it had 10/100 Ethernet and single band 802.11n. It's getting to the point where, if you want to run a router distribution worth a damn, you'll need an x86 computer and multiple NICs.

As for me, I've been pretty happy with the Ubiquiti EdgeRouter Lite, along with a bank of Raspberry Pi units doing assorted little things, including DDNS updating. It's annoying that these things need to be offloaded from my router (Tomato does reverse proxying natively!), but now I can use basically any router with port forwards if I really wanted.

As to the original topic at hand of how to update one's DDNS, that functionality is pretty ubiquitous. Most DVRs and NAS units have many options, including Dyn, No-IP, Afraid.org, and Namecheap. Most of those services also have desktop clients, and even if none of those are options, there are plenty of tutorials for every major DDNS service to be updated by a RasPi Zero.