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Shark gills

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I've noticed that some Roadsters have the shark gills in the front and some don't, going all of the way back to the 2008 models.

Was this just some sort of styling option that buyers got to choose from?

No, that is the new style of the 2.5 models (actually, some "2.25" models were 2.0 models with the new fascia). A 2008 model (aka 1.5) would not have that front fascia unless the original one has been replaced.
 
The reason I asked, is I see 2008 models listed for sale which have the shark gills (by the way, what is the official name for that styling cue?)

So, your theory is that if a 2008 model has these, it means the owner added them later himself to make the car look upgraded?

Here's a couple of examples:

Used Tesla Roadster For Sale - CarGurus

Used Tesla Roadster For Sale - CarGurus

...or because the bumper needed replacing

The new style bumper was, as slcasner stated, introduced with the 2.5 model (although, again as he stated, some of the last 2.0 cars got the new bumper - and other improvements - and were colloquially called 2.25).
 
And the 2.25/2.5 front gills / rear bumper and diffuser were available for a short time on the Tesla webstore / Tesla shop that could be purchased and if you like upgraded on the 1.5 cars. I honestly don't like messing with what the car came with in terms of the main body style and look, I feel it takes away from the car. Only way I'd swap things out is if it offered some sort of aerodynamic / traction benefit.