Jessica Alba's Honest company is not keeping things mellow with a health and wellness competitor it believes ripped off their brand name to boost sales ... according to a new suit.

Alba's company is going after a Colorado company, Honest Herbal -- which makes cannabinoid rich hemp products -- for trademark infringement. According to the docs ... Herbal intentionally jacked the 'Honest' name to confuse customers into thinking its products are associated with Alba's.

Honest Company claims it sent a letter to Honest Herbal earlier this month asking them to drop the Honest moniker to avoid a suit ... but it was ignored.

Honest Company's suing not just for money, but for an order forcing the other company to 86 the name.