What everyone else has mentioned (changing documents, Facebook, etc.) are usually good enough for stealth with the general public, but the only problem I would foresee with being 100%, fully stealth is that some records (of your old name) are pretty much impossible to erase.
Name changes are public record, so someone could conceivably look up your new name and find the old name. Background checks also turn up that kind of information. Credit reports may turn up your old name so long as there are accounts (even closed accounts) on there with your old name. This means potential employers, landlords, etc. could end up knowing that you have gone by a (noticeably?) different name before.
The other aspect is people who you know or have known. Either you end up never telling them and avoiding them completely, or you are depending on them not to out you. Even the most sympathetic, supportive person could slip up and compromise your stealth, especially if you have a cover story to explain loose ends.
