Alien naming assistance.

I remember finding this website a couple of years ago, and it might be quite helpful to you. It can be hard to find a good one in there, but you can keep generating until you find one you like.
fantasynamegenerators.com/mass-effect.php#.V86Q5cvTUwh

If you want "loreish" names, check out these conventions (there's always exceptions and YMMV of course):

Turians tend to have Roman sounding names i.e. Garrus Vakarian, Tarquin Victus, Saren Arterius, Septimus Oraka

Asari have more generic "unique" names but can also evoke classical Greek Names: Atheytha, Irissa, Athame, Rana Thanoptis. A trick I've used with these sorts of names (and I'm sure they've used as well) is taking a common name and changing a few letters around (not just spelling unless you want to Game of Thrones it). For example, Liana is a name I've heard in RL. Change one letter you get Liara. Another commonality seems to be T'[some one syllable word]- a possible equivalent to our Mc, Mac, or o' i.e. McDonald MacLeod or o'Malley. There's probably a word for that, I just can't think of it at the moment.

Salarians tend to have shorter sounding names, possibly to mirror their shorter lifespans. Or if you want in on the joke, take the name of a dev and really mangle it Padok Wiks=Patrick Weeks, Jondam Bau= John Dombrow. The easy thing with salarians is because of their short lifespan you could probably reuse a few surnames if your story's set far enough forward.

Quarians follow a stricter format [firstname]'[lastname] vas [shipname] if post pilgrimage or nar [shipname] if pre-pilgrimage. A quarian without a shipname is likely exiled from the Migrant Fleet. As for the names themselves they tend to be more... non-western for lack of a better term. You can of course get creative with the ship name (Qwib Qwib anybody?) Examples: Tali'Zorah nar Rayya (pre-pilgrimage), vas Neema and vas Normandy (post pilgrimage), Daro'Xen vas Moreh, Zal'Korris vas Qwib Qwib.

Batarians tend to have harsh sounding non-western names. They're pretty generic and not that well documented so there's not much guidance to be had. You can throw in an apostrophe for good measure.

Krogan names are surname first, where the surname is the clan name. You can use existing clans (Urdnot, Gatatog, Jorgal etc) or make up your own. Krogan given names are typically short and to the point, much like the krogan themselves: Char, Wrex, Grunt, Wreav. Clan names can be omitted but if they don't have one at all, they are outcast.

Volus also have really short names. It seems either their first name is short or their last name is (or both): Barla Von, Din Korlack. Having a three letter name somewhere in there is probably good enough.

Elcor seem to have one name only. Possibly because they communicate not just with sound but scent as well, there may be more to their names than just the one spoken word: Harrot, Calyn.

Drell- not enough data. First name last name format but other than that anything's possible.

Hanar- this where you can have some fun. Hanar have face names, general labels strangers use and soul names which are more personal and reserved for close ones. Face names can be anything, soul names are a poetic phrase that sums up the individual. Example: Zymandis (face name), Regards the Works of the Enkindlers in Despair (soul name).

Huh. Learn something new every day.

You're right. Salarian full names are more like addresses of origin: homeworld, nation, city, district, clan name and given name

Turian name: Anitus Sarkeesian.