1) Totally normal name, for a human or for a pet. In canon, Lee Scoresby’s daemon’s name is Hester, Serafina Pekkala’s is Kaisa, Ruta Skadi’s is Sergi, and one of the severed children had a daemon who was flat-out named Ratter.
In the HDM-universe fic I’ve been writing lately, the daemons of the Jewish characters have normal (if old-fashioned) names taken from the Tanakh: Ahisamach, Zephaniah, and Tirzah. Maureen’s daemon is named Dalziel, which looks like it should be the name of an angel, but is in fact a Scottish clan. This hasn’t been mentioned in-story yet, but the Li Huas’ daemons are both named Sapphire.
2) Classical, literary, or historical inspiration. In canon, Pantalaimon is from the Greek name of Saint Pantaleon, and one of the children from the world of the dead has a daemon named Castor. (These can overlap — for instance, Sergi might have been chosen because it’s a modernized form of Saint Sergius.)
In fic, Eustathias (Dana’s daemon) is from the Greek name of Saint Eustace. Vanessa’s daemon is another that hasn’t come up, but his name was Orestes.
3) An evocative foreign-language word. In canon, Will’s daemon gets named Kirjava, a Finnish word for “many-colored.” Lord Asriel’s manservant has a daemon named Anfang, German for “start/beginning.”
4) Start with a target language, mess around with names and parts of speech until you find something that sounds right. Can’t speak for Pullman, but that’s where I got a bunch of names. Josie’s Ojansi has a name thrown together from Finnish syllables; Köhler’s Rozarilde is very German; Henriette’s Clotère, very French. Carlos’s Isaña was named after spending a while in Spanish-language recipe sites.
(Very important to google names like this before using them, to make sure you haven’t accidentally stumbled on a word that means something. You don’t want to be unintentionally scandalous and/or hilarious.)
5) Online fantasy name generators ftw. You don’t need to go to a lot of effort every time, or make every name meaningful. Take your pick of all the generators Google has to offer. I resorted to those for Steve Carlsberg’s Taeminlahn, Renée Carlsberg’s Tovitthae, and Megan Wallaby’s Isidorus.
Final note: Daemon descriptions are more important than names!
That’s because the fewer names you include, the easier it is for a reader to keep up. And if you refer to the daemon by their species and/or the human they’re associated with, you take the burden off your audience of tracking those things too. It’s way simpler and quicker for readers to parse “the golden monkey held Sir Charles’s snake daemon” than “Omuvaryx held S’ctarhaclign.”
(Especially if you never gave your readers a description in the first place. I can’t tell you how many daemon AUs I’ve read that go “Jon came over for lunch with Linicembes. Stephen and Rilleusthi were happy to see him. Olivia called, and Italene said hi too.” And it’s only when you get to the author’s notes at the end that it says “by the way, Linicembes is a fox, Rilleusthi is a ribbon-tailed astrapia, and Italene is a cicada.” Aaaargh. Don’t be that writer!)
So if coming up with names is annoying or taxing, just remember that any given daemon only needs a name if the narrative would get noticeably awkward without it.