According to Microsoft's development blogs, .NET 5 will be the next release name after .NET Core 3.x.
.NET 4.8 (or called .NET Framework 4.8) will be the last major version of .NET Framework. After .NET Core 3.0 Microsoft will not port any more features from .NET Framework.
.NET 5 as a unifying platform for desktop, Web, cloud, mobile, gaming, IoT, and AI applications. It also shows explicit integration with all Visual Studio editions and with the command line interface (CLI). The goal of the new .NET version is to produce a single .NET runtime and framework, cross-platform, integrating the best features of .NET Core, .NET Framework, Xamarin, and Mono (the original cross-platform implementation of .NET). .NET 5 also features Java interoperability on all platforms and interoperability with Objective-C and Swift on multiple operating systems.
.NET Core 3.0 will be released in September 2019 .NET Core 3.1 Long Term Support .NET 5.0 will be released in November 2020