Some days ago, I successfully built my own software. I want it to be open source. Someone told me about the Unlicense license. So, if I publish my software under the Unlicense license, would anyone be able to take credit for my work?
Since the Unlicense doesn't require attribution, downstream distributors are under no obligation to identify you as the author. This is in contrast to most other free and open licenses, which require downstream distribution to preserve your copyright notice. The MIT/X11 license and the BSD licenses are very permissive choices that require attribution.
On the other hand, I would expect that someone falsely claiming your work as their own might cause a civil offense in some jurisdictions and definitely would run afoul of your moral rights (in jurisdictions that recognize them).
That said, it may be legal for a downstream author to omit mention of you as the author while also making their own copyrighted changes. They could then correctly identity themselves as the author of their own changes and choose not to mention the original author. Being craftily selective about which attribution to include may or may not run afoul of the original author's moral rights, depending on your jurisdiction's specific laws.
If "can" means "is able to," someone else can falsely take credit for your work -- and that's not necessarily illegal.
But he can't do it ethically, because plagiarism is unethical.
Plagiarism and copyright are separate concepts:
If you wrote software (or any other type of creative work) and someone else falsely claimed he wrote it, that's plagiarism.
If you licensed your software and required attribution, and someone else redistributed it while falsely claiming he wrote it, that's plagiarism and also a copyright violation.
If you licensed your software without requiring attribution, and someone else redistributed it while falsely claiming he wrote it, that's plagiarism but not a copyright violation.
So in some situations it's possible to plagiarize another person's work without violating copyright law or licensing requirements.