Yes, you can. But you can't take it to the patent office (register a trademark or anything). Also, while you use it as a logo, you must keep the subscription active or provide an attribution link to Icons8, complying with the Icons8 License.
Why you can't register such a logo
According to the Icons8 License Agreement, we provide digital assets under a non-exclusive license. This means that while you have the right to use the assets, so do other users. Here are the key points to consider:
License restrictions. You can use the assets, but Icons8 retains ownership, and other users can use the same assets.
Respectful use. Icons8 expects users to use the assets in a manner that respects the company's and third parties' intellectual property.
Copyright infringement. Icons8 icons are copyrighted. You have a license to use the icons, but Icons8 retains the copyright to icons we created, and respectful owners retain the copyright to the free icons created by the community's requests (like logos and characters).
We encourage you to contact a legal professional for advice tailored to your situation.