Puns , definitely

I tend to use names that hint a characters personality, or are diametrically opposed to the character role in the story.
Such as calling an evil character Angelo, or Goodman.
My favourite name I ever used was for a corrupt arms dealer named Hephaestus Finger, a bit pretentious but effective.

My characters come to me and tell me their stories.

Depends upon the tone of the book...In my first book (suspense), I used the maiden names of my lab co-workers as character last names. My second (humor) used the names of my friends' dogs (which worked out well, since the characters didn't need last names anyway...).

The story bits (plot, location, ethnicity of characters) are often enough to conjure a name.

But if not, once i have an image of the person i explore their heritage. When and where were they born?

Then baby name databases for that year and in that place are useful.

I struggle with this too. I really like what everyone has said thus far. I have a list of names, that for some reason or another, strike my fancy, and/or sound good/interesting to my ear. Then there are staples, like the telephone book (yes they still produce hard copies...lol), and as has been mentioned, tons of resources on the internet.

The bible, the stock exchange, headstones, newspapers, novels, my imagination,

I believe that there's a tradition that the names are based on places and places based on names?

I come up with several names all the time until either one stands out or a combination of them sounds right, then I build the character around their name. Their names are my anchor to their personalities. I find it also makes them more memorable.

I find it distracting to worry about character names. I like not characters without names, though names can be valuable if they add variety, they certainly keep the characters' identities straight in the mind of the reader and the writer. Well, sometimes names occur, some story ideas trigger names instantly, others you must dig into before a name can occur to you. It's part of the organic flow that occurs in pre-writing, but story and character and their interplay matter more than the names of particular things. That, however, is not a hard and fast rule for me. Sometimes a story idea comes from a given name of a thing. Mostly though, at least for me, the story germ has to grow organically before I can begin to see the leaves and the fruits and flowers and come up with names for them.

It's a mix of all the above. In my pantomime, Wizard Prang and Witch Hazel seemed good, fun names. Dyslexia, their adopted daughter, is so called because, despite intensive lessons, she is not very good at spelling. Des Torneador is a handy man (destorneador is Spanish for a screwdriver).
In some stories many characters have no names. It's all a matter of "individuality" in your writing.

All of the above. A lot depends on the role, origin of the character, and the type of story.

I suppose it’s a combination. My latest character I picked from baby names and then my dad looked it up and the name, Cassandra, was,in Ancient Greece/Rome, a woman who knew the truth and no one believed her. It was so perfect.

When I make up a name, I'm not always sure whether I just make it up or it's a name the character wants. Likely both, but ultimately, aren't they the same thing?