I am answering primarily with regard to the U.S. Lanham Act (15 U.S.C. § 1501 et seq.) and state trademark laws in the U.S., but except as noted, these concepts are widely honored internationally in trademark law.
As a general rule, generic names cannot be trademarked. Thus, you can't trademark "liquor store" for a liquor store, or "Calendar" for a calendar, but you might be able to trademark "liquor store' for a copying machine line, or "Calendar" for a perfume.
Sometimes a trademark can be obtained for a stylized logo incorporating a generic name (e.g. "liquor store" in bold pink 48 point comic-sans), but to be valid, the trademark must disclaim any assertion of rights in the mere genetic words themselves.
Also, sometimes a trademark that is descriptive but not truly generic, like "Palisade Red" for red wine made in Palisade, Colorado (as opposed to the truly generic name "red wine"), can acquire what is known as a "secondary meaning" through exclusive use over a period of time while registered with the Patent and Trademark Office, without contest from anyone else. If it meets these requirement it can win an entitlement to trademark protection. But, the nuances of this particular route to trademark protection are particular to U.S. Lanham Act (which is the name of the federal trademark law in the U.S.).
Domain names and entity names in a particular jurisdiction are somewhat different. While it is possible for two competing products or firms to share a generic name, it is not possible for two owners to have precisely the same domain name or precisely the same entity name in the same jurisdiction, even if the firms seeking the same name sell completely dissimilar types of products.
For example, there can only be one: "Calendar.com" domain name, even if one company uses the name "Calendar" to sell calendars and the other company uses the name "Calendar" to sell perfume.
In those cases, however, it is relatively straightforward to determine what names are and are not taken.