I've thought about this very question and for years I was adamant that deconstructing yourself and then reconstructing elsewhere meant you were killing yourself and then creating a clone.
Recently, I realised that this DOESN'T MATTER.
Our definition of 'death' is insufficient to describe the universe where this power is possible. You are disassembling yourself and then reanimating your constituent particles. The point at which 'death' occurs isn't strictly relevant, even if this doesn't happen instantaneously (which I assume it does). There will be a gradual change from animated and thoughtful, some momentary confusion and then you'll 'come to' somewhere else.
If you've ever had a dreamless sleep in a moving vehicle, this is the same thing as far as you're concerned. You don't have memories of the travel and you're basically the same person as when you started (but crucially not the same - we change at every level, every second of every day).
It's hard to divest ourselves of the idea that we won't be the same, but we forget just how often we undergo consciousness dissolution via sleeping, drugs, anaesthetics etc. Imagine someone in a coma for 5 years. No brain activity, no physical movement. They've travelled millions of miles around the sun, the galactic core etc. Their entire body (give or take a few bits) has been replaced and yet they are still the same person when they awake. They might feel a bit odd, but they are still 'them' and they'll accept it eventually.
Death, actual death, is the slow atrophy of brain function resulting in irretrievable destruction of the mind and no way to bring it back. Even if we could (with some Star Trek tech, rebuild the broken neural connections etc.) then that would be largely the same as teleportation. i.e. molecular reconstruction, specifically the re-building of the individual from the 'buffers' (cached physical image).
I imagine people teleporting in the future will feel nervous in the same way as people about to undergo general anaesthetic. They fear that 'they' won't map to the new state, but they'll do it anyway and the person who's left at the end will accept their situation just like patients do today.
We're basically the cognitive inertia represented by our memories, and while (as one comment suggested) it's possible to hijack our pattern in transit and reproduce it at will, there is only one set of particles making the trip and the others are simulacrums. They won't know that, though... So be nice.
Update: (thanks to Rozenn and Forest's comments). Some parts of our bodies do NOT undergo change over time, and could in fact be traced to before our birth, right until we die of old age. However, the broader point still applies, it's just not true to say that 100% of our bodies undergo complete replacement/renewal. It's likely around 99.9%, but that doesn't seem to relate to anything that could be called 'individual', as the molecules that have persisted aren't protected in any way, they just got lucky and could go at any moment.