The thing about backgrounds in D&D 5E is this: they’re strictly past-tense.
They’re not what you are — they’re what you were. What you are, now, is an adventurer.
The most important question to ask about your background is what changed? Why did you stop doing whatever your background describes and start adventuring? — Player’s Basic Rules, pg 36.
The official backgrounds, unsurprisingly, pretty much get this right. Perhaps also unsurprisingly, a lot of fan-made backgrounds are starting to mess this up. Just something to keep an eye out for.