Our society is going through a state of transition regarding marijuana. Be aware that state law and federal law sometimes contradict each other. When that happens, federal law usually trumps over state law. The Controlled Substances Act of 1970 lists marijuana as prohibited.
In 2005, Gonzales v. Raich, the US Supreme Court held that federal laws banning marijuana throughout the United States override any state law that attempts to legalize it. This means that you could face criminal penalties in federal court despite state permission. The current presidential administration has indicated that they are not as concerned about going after people who hold state marijuana licenses as previous presidents - however I have heard that the arrests and prosecutions continue. Our society is likely to change in the near future, but I cannot honestly tell you that selling marijuana is 100%. Are there people operating marijuana businesses openly? Yes. But as a lawyer it is my duty to inform you that it carries a risk of criminal prosecution and asset seizure.
Thus, because federal law prohibits marijuana, the safest choice is to avoid the marijuana business.
My advice is directed at California cases since that is where I am licensed; otherwise all advice is to be taken only as an answer to a hypothetical California matter. Advice given here does not create an attorney-client relationship. My comments should not be considered a replacement for brining more detailed facts about your issue to a lawyer who practices in the area of law in question.
The First Amendment protects your right to free speech, and I believe it would not be illegal to use the word "marijuana" in a store name or advertisement. But the wording will probably attract law enforcement as well as customers. You do not say whether you will actually sell marijuana, though it is easy to imply that. I think you will soon be visited by the police and federal government, who will want to know what you are selling, and who will arrest you and close you down if they believe what you are doing violates the law.
The response I have provided is general in nature, and does not create an attorney-client relationship. My practice is based in Rhode Island, and the law and practice in other states or jurisdictions may be different.
The answer is you probably can, but at your own risk, as your store (and you) may be seen as attempting to sell or indeed selling marijuana. I think doing so would be a very bad decision if you are worried about wasting your money. Your store will attract attention from those you least want attention from - both federal and state law enforcement. Not a wise idea.