Yep... I name 'em. Mostly because it makes them far easier to tell apart on networks and the like. Mobiles too, since bluetooth came along.
Given that it's usually a good source of names to go with a theme, and I was a massive anime head at the time, I went Ghibli and have stuck with it since.
First desktop to actually get networked was Totoro. Because it was a big, slow monster that made a lot of noise, but I loved it all the same.
The cheap crappy laptops I had at first just got their model names, because I didn't care that much for them and they were hardly ever connected up

(Acer NL350 and 370)
My "good" laptop (which I still have), Nausicaä. Seemed a natural progression. Also small, light, surprisingly powerful, had a bit of a split personality, was eco friendly, and ... ahem. Good to touch.

(it was a ultraportable convertible tablet)
Phones along the way have kept the theme up - Yupa, Teto, Teto2 (meh!), Kai and Kui, as they were all "paired" with the laptop. I'm going to have to diversify on my next purchase I think... Maybe a new laptop before I get a new phone. Because we have to then get into more minor, or incongrously larger/more influential characters, and it just won't feel right.
Work desktop just has an asset ID number. Which is appropriate; if it was a person it'd be a complete tool also.
I don't call them by name however. That's just loopy. It's always "the phone" or "the laptop", or in extreme cases the brand or model number.