Mythological name and properties of lemon balm?

As far as mythical properties go, lemon balm was most often used as an ingredient to draw love, lust, and friendship to a person, at least in the Western tradition. It as almost everything, can also be used for protection.

Lemon balm ( Melissa officinalis ), a member of the mint family, is considered a "calming" herb. It was used in the Middle Ages to reduce stress and anxiety, promote sleep, improve appetite, and ease pain and discomfort associated with digestion (including flatulence and bloating as well as colic). Even before the Middle Ages, lemon balm was steeped in wine to lift the spirits, help heal wounds, and treat venomous insect bites and stings. Today, lemon balm is often combined with other calming, soothing herbs, such as valerian, chamomile, and hops, to enhance the overall relaxing effect.

Darkcat is 100% correct.

As for alternate names, the only one I'm aware of is Melissa.

Lemon Balm's botanical name is Melissa Officinalis - which I'm quite used to seeing abbreviated to simply Melissa.

Maybe that's the name you were looking for.