Is there a transmog-like service?

And if so, how do I access it?

Is that WoW-speak for glamours? (Modifying one piece of gear to look like another)

You have to reach Lv50 before you're allowed to glamour. At that point, a quest in Mor Dhona unlocks it.

I assume you mean glamour, which is giving one piece of gear the appearance of another. Yes, you can glamour, but not until level 50 when you complete a quest for it.

As the above posters have said, yes there is a glamour system in the game, it's not available til you reach level 50 though, as the quest to unlock it only becomes available upon reaching that level. The quest in question is 'A Self Improving Man' from Revenant's Toll in Mor Dhona, and once you unlock it, you simply need to purchase a consumable item called a 'glamour prism' for each piece of gear you want to glamour (the gear is not lost when you glamour but the glamour prism is). You also need to use the glamour prism that matches the type of gear whose appearance you wish to use (like, a clothcraft glamour prism is needed to glamour a piece of gear repairable by WVRs).

Til you reach that point however, you can still customize your equipment to an extent by unlocking gear dyeing which allows you to change the basic colour of most types of armour, the quest for which can be unlocked at level 15 from Vesper Bay - the quest to do so is 'Colour Your World'. Gear which can be dyed has a small coloured circle on it's icon that denotes the colour it is currently dyed as (if it is not dyed the circle will be clear).

Also if you join a Free Company, you can add their logo to certain gear by speaking to the npc 'OIC Officer at Arms' in each Grand Company HQ and paying a small fee. Hopefully this has helped. :D