Note that you are very unlikely to get the trademark for the name of a free program anyways. Just claiming that the term is a trademark of yours has no legal meaning if you cannot prove that you actually trade using that name. Giving stuff away for free is not trade; you must have received something in return, even if it is just $1 or some other kind of consideration.

And your trademark will only be protected in the geographical location where your trade is taking place. If you "sell" a license to your buddy in the same city, you will not have a valid claim to the trademark outside the city.

One way around this is to register an "intend to use" trademark. But this will cost money and must be renewed every year.

Unlike patents, there is no "prior art" in trademark protection. Just because you use a term for your free software does not prevent someone else from using the term for an unrelated product and them starting trading using this term. They will then have a valid claim on this term as their trademark and can ask you from using it if there is cause for confusion of their customers. The fact that you used the term first is irrelevant if you didn't "trade" under it and didn't register it.

Given all this, I wonder if using a descriptive term isn't a better idea: it makes it less likely that someone else will claim it as their trademark later and force you to change your name again.

As expected, the above does not constitute legal advice, yada, yada, get a lawyer to get a qualified legal opinion.