Dragon Warrior was always called Dragon Quest, but there were some copyright issues ir something like that, so it was re-named to Dragon Warrior. Since then, things have changed and it's regained it's normal name. A game VERY similar to Dragon Warrior (Dragon Quest) is of course Final Fantasy, if anything, the games are so-alike it's not funny. If you've already tried Final Fantasy, try out Chrono Trigger or Secret Of Mana, these 2 games are probably the best RPG's you'll ever play.
Chrono Trigger is a very good game and may I know which system you are referring to? Retro or new console?
Dragon Quest's North American name was changed due to a trademark conflict with the role-playing game DragonQuest, which was published by veteran wargame publisher SPI in the 1980s until the company's bankruptcy in 1982 and purchase by TSR, which then published it as an alternate line to Dungeons & Dragons until 1987. In 2003, Square Enix registered the Dragon Quest trademark in the US, making the Dragon Warrior name obsolete....thus saith Wiki.
Yes. it's been Dragon Quest in the USA for 6 years now. I hope we never have to see Dragon Warrior again And for anyone looking for a great RPG games to play on DS, I highly reccommend Dragon Quest V. You won't regret it.