When writing code, I tend to use the word "write" in this case. When I do that, I try to use the word "read" as the opposite (getting information from the database). I've also been known to use "load" and "save", but the problem with "save" is that there is no "save as", so the concept of File / Open and File / Save doesn't always make things clear.
UPDATE:
I went searching and the technical term is "persist", as in you "persist" to a "datastore" (either a database or a file or anything else where data is stored). As far as I know, nobody has (yet) used persist to only mean "update" or "insert". It isn't as common as "save" or "write", and the technical meaning isn't one you'll find in most dictionaries, but at least it is a real English word that native speakers will know and understand.
"write" was used as "update" in file modes: r = read, w = write, a = append.
So I guess I had better go back and change write to persist in the code I wrote yesterday.