OK, actually I've emailed D. Richard Hipp a few months ago asking for permission to use the name UnQLite in a future open source project, here is a copy of Hipp's reply:
It would be good if you can make it clear on your website, somehow, that
yours is an unaffiliated project. Otherwise, people might go complaining
to me when they find bugs in your code. (Don't laugh - that sort of thing
happens a lot.)
Other than that, you are welcomed to use the name.
You might want to have a look at the LSM storage engine that Dan Kennedy is
working on for SQLite4. It is faster than the clunky and dated B-Tree used
by SQLite3. It is also faster than LevelDB. And it supports nested
transactions, with rollback. And concurrency. And it is more NAND-flash
friendly. See http://www.sqlite.org/src4/timeline for the latest code.
It would be good if you can make it clear on your website, somehow, that yours is an unaffiliated project. Otherwise, people might go complaining to me when they find bugs in your code. (Don't laugh - that sort of thing happens a lot.)
Other than that, you are welcomed to use the name.
You might want to have a look at the LSM storage engine that Dan Kennedy is working on for SQLite4. It is faster than the clunky and dated B-Tree used by SQLite3. It is also faster than LevelDB. And it supports nested transactions, with rollback. And concurrency. And it is more NAND-flash friendly. See http://www.sqlite.org/src4/timeline for the latest code.