Still think it's ridiculous to require you to have a conlang!
The problem of "name"-ness is one that I run into a lot with my randomly generated words. Some words just don't look like names at all, while others are better--although it is hard to tell how much of this is purely subjective judgement. The way I come up with names is to create a lot of words, and then pick the ones that strike me as having a certain name-y quality.
If I was in your situation, this is what I would do: Pick a language that you like the look of. Find a text in that language and do a rudimentary analysis of it, such as what letters occur and in what sorts of combinations. Keep in mind that the simpler the syllable structures, the easier it will be to do this--it's far easier to write down the rules for Japanese syllables than it is for English.
Then use what you find out as the basis of your "language." Create a lot of words according to those rules, either just by brainstorming on paper or by using a random word generator program, and pick out the ones that you like the most.
One other thing that helps with namey-ness is to pick real names, and then just modify them a bit. You can modify them according the rules of this language you like, and swap out some consonants and vowels, and voila!