Basically, yeah. Every Gym Leader has a pun in their name derived from the type they specialise in.
Brock = "rock". Self-explanatory.
Misty = "mist", normally a form of water. However, Misty is a frequent anime character so such a normal name may be because they wanted him to have a normal name throughout the anime to cause less confusion. This may apply to Brock as well.
Lt. Surge = "surge", as in an electrical surge.
Erika = "erica", a type of flower.
Koga = "kogaryu", a ninja school.
Janine = "ninja". You know, take away the 'e' and it's an anagram of ninja. Seems legit. She is the Koga's daughter, so that demands some ninja-ness.
Sabrina = I don't really know.
Blaine = "blitz", "blaze"... you get the jist.
Giovanni/Blue = Giovanni is the Team Rocket leader so it seems there may not have been a direct pun on his name. Blue has various types. However, Giovanni has "geo" in his name, which is a frequent reference to geography, or ground, his specialty type.
Falkner = "falcon", a type of bird.
Bugsy = "bug", self-explanatory.
Whitney = What you said, "white" which is a 'normal' colour.
Morty = "mort-", a common prefix that is relevant to life. E.g., 'post-mortem', 'mortal' etc.
Chuck = "Chuck Norris", a karate dude.
Jasmine = "mine", mining minerals.
Pryce = I would have said reference to "ice", but his name is spelt with an 'i' so it may be wrong.
Clair = a suggestion stated "lair", as in dragon's lair. I don't really know how this comes into play, but it seems to make sense I guess.
Roxanne = "rock". Self-explanatory.
Brawly = "brawl", a way of fighting.
Wattson = "watts", a measure of electricity.
Flannery = "flame", "flare", something beginning with "fla-".
Norman = "normal". Self-explanatory.
Winona = "wings", the way birds fly. :P
Tate and Liza = "meditate", maybe? I don't know one for Liza though.
Wallace = "wallow", maybe. A way of crying, which may refer to water.
Juan = Dunno. I seriously dunno.
Roark = some pun on "rock".
Gardenia = "garden"
Maylene = "melee", a type of fighting style.
Crasher Wake = It sounds pretty cool, and "wake" may be some pun on "wave" or some other form of surfing or something.
Fantina = "phantom", a type of ghost.
Byron = "iron", a type of steel.
Candice = "ice"
Volkner = "volt", a measure of electricity.
Cilan = "cilantro", a type of plant. This is probably true, as cilantro is another word for coriander, which is a type of herb. This matches Cilan's ability to cook.
Chili = "chilli", a hot substance, which probably relates to fire.
Cress = maybe short for "watercress".
Lenora = "normal"
Burgh = "bug"
Elesa = "electric"
Clay = "clay", a substance that comes from the ground. Gee, Unova Gym Leader Names are pretty damn creative.
Skyla = "sky"
Brycen = Like Pryce, maybe a pun on "ice".
Drayden = "dragon"
Iris = "iridescent", possibly. But, again, another anime character that may warrant for a normal name.
Roxie = This may be a pun on her professsion, a "rockstar".
Marlon = "marlin", a type of fish that is known for swimming very fast.
Viola = "viola", a type of plant. This may seem to go well with bugs. This is also true as a pansy is also a type of plant, and also the name of Viola's sister.
Grant = "granite", a type of rock.
Korrina = apparently it means "athletic girl". I've never heard of it before unless it's some other dialect but whatever. I have a few people confirming it so I guess it's right. :P
Valerie = apparently this name comes from "corn salad" and "faerie" (which is German for fairy, Valerie's name is the same in both English and German.) I don't know how corn salad comes into this, but it's Japanese name 'maashu' means 'corn salad', so... o_o
Clemont = this probably comes from "lemon". Again, have no clue how it relates, but it's Japanese 'shitoron' has 'shito', from 'shitorasu', which means "citrus". Maybe that's his favourite food. :P
Olympia = "Olympus", as in "Olympus gods". She may have some relation to this, having her godly appearance.
Wulfric = his appearance may relate to "wolf".
But those are all the gym leaders addressed. If anyone can help me fill in the blanks that would be nice.
Hope I helped. :)
Source, Bulbapedia and the commenters who helped. Thanks.