According to the brief FAQ, only characters who are level 40 or under and haven’t logged in since October 5th of last year will see their names at risk. The best way to preserve your name is to either log in or get that character to level 41 or higher.
When the Great Unnaming arrives on May 10th, Trion will also launch a character name service for those who want to take one of the freed up names or make a new one.
Source: ArcheAge