By coincidence, if my company was “Internal brilliance method”(I just made that up) could IBM(international business machines) sue me over trademark infringement? In different industries different look, would they have a solid case?
A trademark is specific to an industry or type of products or services. And, while it is virtually impossible to get a new trade name with a three letter acronym because almost all of them are taken, three words that start with the same letters as a three letter acronym is not infringement on the acronym.
You might very well be infringing if you used "I.B.M." to sell computer equipment. But, "Internal brilliance method", spelled out, would not infringe I.B.M., even in the computer equipment industry, and "I.B.M." in the food service industry, for example, would not be trademark infringement on the International Business Machines" trademark of "I.B.M." for good and services of the type that it offers.
In general, if a person or firm uses a trademark, or a word, phrase, logo, or symbol that is similar to a trademark to promote, market, or identify goods or services (products), and reasonable consumers could be confused into falsely thinking that the products come from the same source as that identified with the trademark, or are approved, endorsed or sponsored by the trademark owner, then there may be trademak infringement.
This is further limited by the category of the product. A trademark "Komodo" for a brand of shoes would not normally be infringed by "Komodo burger" for a brand of fast food. "Jiffy Lube" for oil change services is not infringed by "Jiffy printing" for print services.
If a mark is "well-known", or "famous" however, protection may be extended into unrelated areas if there is a likelihood of confusion. See the page "Well-known marks" from the US Patent and Trademark Office (USPTO), which says (in part):
The [Lanham] Act protects a mark against infringement or registration by another party's similar mark for goods or services that are the same, similar, related, or even unrelated if there is a likelihood of confusion, whether or not the senior mark is registered.
The owner of a well-known mark may bring an action in U.S. federal court for trademark infringement under Section 43(a) of the Lanham Act. The court will make a determination as to likelihood of confusion in deciding infringement. U.S. case law outlines a variety of non-exclusive and non-exhaustive factors that can be used in the analysis. ...
A name whose initials mach a three0-letter trademark, such as “Internal brilliance method” matching "IBM" or "For My Future" matching "FMF" is probably not similar enough to cause confusion, but that is a matter of fact and may differ in each case. The more similar the nature of the new product is to the nature of the existing trademarked product, the stronger the case for an infringement action.
Note that trademarks are usually national in scope. A trademark registered or protected in one country will not automatically be protected in another, although an owner may take steps to protect it in many countries. However, marks that are "well-known" in one country may be protected against registration or use in another without permission.
Disclaimers making it clear that a mark is different from a somewhat similar mark may help to avoid confusion, and thus avoid infringement claims.