The topic you posted under is trademark infringement which has to do with violating someone's trademark. I have changed the practice area to trademark application, which is what you need.
This is not legal advice. You should always discuss the specifics of your issue in person with an attorney. Be aware that there are time limits on all claims that depend on the kind of claim, so do not delay in seeking an attorney.
This has already been answered here at least once before
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Consider consulting with an attorney.
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This is really a very fact specific question. You may be able to do what you are describing, but it may also be the case that you can cross the line and expose yourself to a legal action.
Your best bet it to consult with a lawyer in private and get specific guidance once all is clearly understood. Most of us here, including myself, offer a free phone consult so you may want to take advantage of that.
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If the question is whether you can sell the clothing as "recycled", in the absence of a particular statute in Texas dealing with this, it would not be a misrepresentation. You may want to come up with your own name and logo and copyright and/or trademark the name. You could also incorporate (recommended) and use the unique name you invent. You can check the TX Secretary of State data base to see what other names are in use. You can also check the U.S. patent and trademark data base.
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The reason I think that you were correct in assigning this question to trademark infringement is the possibility/probability that existing trademark(s) exist on the clothing. I had a client doing precisely what you are describing with vintage, barely legible, Harley Davidson apparel which he significantly modified.
Short version - all "heck" broke lose. Depending on the unhappy original trademark owner, you may win in court, but the experience of victory may bankrupt you.
The above is general legal and business analysis. It is not "legal advice" but analysis, and different lawyers may analyse this matter differently, especially if there are additional facts not reflected in the question. I am not your attorney until retained by a written retainer agreement signed by both of us. I am only licensed in California. See also avvo.com terms and conditions item 9, incorporated as if it was reprinted here.