So I have a suffix at the end of my name. Like kings and stuff (think King Bob III).
It gave me a bit of trouble in the US but not much. I existed twice at the DMV. One was me without the suffix, one me with it. It's on my birth certificate. It's after my last name. However I do not consider it my last name. It's a suffix, kind of like a title that's built right into your name (but one you don't have to mention).
In the US despite the complications (like existing twice

which I fixed with a trip to the DMV) suffixes are optional when it comes to legal documents. Obama for example has a suffix in his name but doesn't write it down every time.
Now I move to the UK and I'm told nobody has ever heard of this outside of kings and crap. Dunno how true it is but at the same time nobody seems to know how to work with a suffix. Despite me trying to keep things all the same it seems like people have handle it different ways. Now across the board I'm known as "LastName Suffix" or "LastName" in whatever random government thing there is.
I've been told that I absolutely NEED to have the suffix in there since it's on my passport and work permit. However I freakin' hate that. My suffix isn't part of my last name... But I tried it anyways. However people still randomly included it or not. I have no idea what kind of issues this could cause, if any, in the future. I've been told that it could cause issues but I've gotten no details. Maybe it won't. Anyone have ANY experience with this?