All assets capitalised should be impairment tested annually - it's basically to ensure assets are not being carried at more than their recoverable amount. So it applies to assets with a definable useful life, and to other assets that have an indefinite life. Remember that if the reason an asset is impaired no longer applies, then the impairment can be reversed - with the exception of goodwill, which once impaired, cannot be reversed.
To provide a direct answer to your question. Yes, because it has an indefinite life. A trademark can have an indefinite life if the trademark owner keeps re-applying for the 10 year exclusive use rights. So if a company decided to discontinue a trademark then its cost would be amortized.