As the question says if a user of a particular wordmark breaks his word into 2 and uses it on goods sold(tm is engraved on goods) then can he seek protection in case of potential infringement.
The person could seek protection, but could well be unsuccessful. Such a person should register the separate parts of the word mark separately. An application for such registration might or might not succeed, of course, because the partial word mark might be ripe for confusion with an existing word mark.
For example, if word mark is "Neighborhood Pizza," and the owner wants to use the word mark without the first eight letters, and there is already a company selling pizza under the mark "Hood Pizza," then what you propose will certainly fail. On the other hand, if there is no existing word mark that can be confused with the altered word mark, then the bid for protection might succeed. As with any trademark, of course, protection will be more secure if the mark is registered.
The primary question for infringement is whether it creates a "likelihood of confusion" among the consumers. As a general rule, the phonetic equivalent is deemed to be "the same brand". In fact, even an image or a foreign word having "the same appearance, sound or meaning" could be ruled "identical", if it gets litigated.
For instance, the brand formed by the words "GOLD STAR" is "the same" as the brand "STELLA D'ORO" and even the "same" as a brand comprised of a picture of a gold star, for purposes of evaluating similarity of brands. Also, an "ANCHOR" brand bread could be infringed by someone else later selling bread or related goods in an overlapping market in a package showing the shape of an anchor.
Under US law, a state or federal registration is completely optional for enforcement of a brand that is "in use in commerce". Whether the owner of a registration for a brand that is not "identical" to the one in use can benefit from the registration priority would be a slightly different question. At the very least, the USPTO examiners will continue to deny applications for registrations that are "confusingly similar" to what is registered, using the "appearance, sound and meaning" tests.
To take it to court and prevail, you would have to own the trademark on whatever wording you are using.