There are a number of issues to consider.
First, to answer the main question: you are legally allowed to use any abandoned open source project, the fact that it's abandoned doesn't change your rights.
Second, the fact that it's abandoned doesn't change its owners rights; in particular, copyright remains with the creators. But for an open source project that isn't particularly important, unless you wish to change the license. (Note too that in some jurisdictions copyright is non-transferable, or not fully transferable.)
Third, there's the issue of continued maintenance. Of course you can fork an open source project; in the vast majority of cases you can continue using the same name etc. What will be more difficult is recovering the original web sites if any, source code repositories etc. If the original maintainer(s) is/are still reachable, you can try asking them; if they haven't disappeared off the face of the earth there's a fair chance they'll be happy to pass the maintenance on to you! If they're not, and the hosting company (Sourceforge, Github etc.) don't have a process in place, things will be a bit more complicated: you'll need to contact various sites and organisations where the software you're taking over is mentioned, and tell them about the change. Generally speaking once you've proven you're a worthy maintainer, the transition will happen, and your new web site or code repository will end up being considered the authoritative source for the project. This becomes much easier once your new versions of the project are adopted by downstream distributions...
I did this a while ago for the Linux console project; it was dormant upstream, and I was maintaining the package in Debian, adding more and more patches as time went by. At that time Sourceforge had a process in place for requesting a maintenance change; they contacted the original maintainer who OK'd the transition, and I became administrator of the Sourceforge project. No copyrights were changed: the original copyrights remain in place on the pre-existing code; but given that I had (and have) no plans to change the license, that's not an issue.