A phrase which is too generic or in too wide currnt use to be a valid trademark, may nevertheless be used as a business name or slogan.
For example "Good Pizza" is so generic that I am reasonably sure that it could not be registered as a trademark, but a business could use that as a name or slogan. A business that did so would forgo any of the advantages of trademark protection or of having a clearly unique name, but as no one else owns trademark rights to the phrase either, no one could sue such a business over its choice of name, or not with any hope of success.
Similarly, if a phrase taken from a meme cannot be registered, no one else can have it as a trademark, and so no one can sue successfully.
As to copyright, names, titles, and short phrases are simply not protectable by copyright at all. See the US Copyright office circular 01 "Copyright Basics" which says on page 2;
Copyright does not protect ... Titles, names, short phrases, and slogans
Circular 33 "Works Not Protected by Copyright" says on pages 2-3:
Names, Titles, Short Phrases
Words and short phrases, such as names, titles, and slogans, are uncopyrightable because they contain an insufficient amount of authorship. The Office will not register individual words or brief combinations of words, even if the word or short phrase is novel, distinctive, or lends itself to a play on words.
Examples of names, titles, or short phrases that do not contain a sufficient amount of creativity
to support a claim in copyright include:
- The name of an individual (including pseudonyms, pen names, or stage names)
- The title or subtitle of a work, such as a book, a song, or a pictorial, graphic, or sculptural work
- The name of a business or organization
- The name of a band or performing group
- The name of a product or service
- A domain name or URL
- The name of a character
- Catchwords or catchphrases
- Mottos, slogans, or other short expressions
... if we can be sued outside of trademark or copyright reasons
Trademark and copyright are basically the only kinds of suit likely to be brought over a business name, logo or similar identification, particularly in the fact patter discussed in the question. (However, see the section on "fraud" below.) Things that are in the public domain are free for anyone to use, not protected against anyone's use. What is not permitted is trying to claim an exclusive right to PD items., by a copyright or trademark claim.
The one exception I can think of is that if someone had established a phrase as a trademark, and it later became a meme, then perhaps the trademark owner could sue over uses of it. But with the phrase having become generic, it might well lose any trademark protection.
The first thing a plaintiff must do in presenting a trademark suit is establish that the mark is a currently valid trademark, owned by the plaintiff. If the mark is not a valid tm, the suit is over because it has no protection.
A comment states:
... Intentionally misleading others to believe you are a particular party using a non-protectable name, when in fact you are a different party, seems like fraud, and it very much hinges on the name/similar identification.
In the fact patter from this comment, the name is derived from a meme, and so there is no other particular person. In that case one cannot plausibly be deceiving anyone into thinking that a business is actually a different business, because there is no business which is uniquely identified by the name.
Still, it is possible for fraud to occur in a fact pattern similar to this. Say a local store calls itself "good pizza", a name not protect able as a trademark, because it is too generic. But it is popular and has a good reputation. Another store, hoping to confuse customers, calls itself "Goode Pizza". A customer calls "Goode Pizza" and aks "Are you the Good Pizza on George Street?" (which is the location of the first store. An employee answers "Yes" (falsely) and the customer then places a delivery order. That might be fraud.
For a fraud case, in most jurisdictions, it must be proved that:
- A person knowingly made a false statement (or in some jurisdictions an intentionally misleading statement");
- with the intention of getting a financial advantage, or depriving another of an advantage or benefit;
- The statement was material to the transaction (meaning that the other party might well have not agreed to the transaction, or demanded different terms, in the absence of the fraudulent statement);
- The other party relied on the fraudulent statement;
- it was reasonable for the other party to rely on the fraudulent statement; and
- harm was done to the other party as a result of this reliance.
Some jurisdictions omit or modify some of these elements.
In the Good Pizza / Goode Pizza scenario above, ther is a knowingly false statement. Since the customer asked about the identity of the store, it can be assumed that it was material to the transaction. The imitation of the other store's name suggests an intention to mislead, although more proof might be needed. There was reliance, and it was probably reasonable. What is not clear is the harm done -- additional evidence might be needed on that element. This scenario is, however, rather different from the situation discussed in the question.
Note that in the US, trademarks can be protected from mere use, without registration, if they otherwise qualify. In general there will be a preference to frame such a case as one of trademark infringement, rather than fraud, if possible, because fraud is usually harder to prove (trademark infringement dose notr require proof of intention to mislead nor of knowing falsehood), and statutory damages may be available in a trademark infringement case, without any need to prove actual damages. Also, the competing store would generally not be able to bring a fraud case, only the customer who was mislead. could do so