I usually aim for a normal first name that fits with the characters background. (So if they're German, a German name. If they're American, an American name). Then I add a last name that sounds plausible for their culture, or plausibly represents the presence of a second culture (due to immigration or mixed parents). For English/American names, I usually go by natural features, colors, etc. for last names, usually two of them put together with perhaps one of the two words mangled up to emulate 'linguistic evolution'. Marshland, Greenstone, Riverwind(Kind of sounds fantasy? But I'd like it if it was fantasy story!), etc. Evolved forms might be, Marland, Grestoe, Riewin.
As you can probably tell, I'm decent at making English sounding names, especially last names. If I'm doing a name for a culture I don't know very well, I usually start to google for a good name. Top 100 baby names from X country. I'll usually choose something on those lists that also sounds good to my western biases, then google last names from a given country, mangle them a little to create a unique last name and bam, there's a last name.
If it's fantasy/sci-fi, I can of course just go nuts, hah. I usually use methods similar to the above, but with less restrictions. 'Evolving' names is usually super fun when doing fantasy/sci-fi, even when making first names.
Is it important? Nah, not really, though I do find it fun to come up with a name. I will say though, I don't like characters names that are super convoluted. So I usually stick to names that are shorter and more easy to 'figure out' even if they are unique. Tonkarr, could be example. 2-3 syllables, usually. Nothing wrong with just 1 syllable, it's just limited what you can do with that. 4 syllables is potentially too convoluted, though it can fit well with some cultures or with a lot of simple syllables (Japanese names, for example). 5+ and we're likely to have gone too far.