Initialize the logger in the constructor:

class SomethingAbstract
{
   protected ILogger Log { get; }

   protected SomethingAbstract()
   {
       Log = Log.ForContext(GetType());
   }
}

Or another variation, if you want to ensure messages from the base class are tagged with that type:

abstract class SomethingAbstract
{
    readonly ILogger _log = Log.ForContext<SomethingAbstract>();

    // Here's your base class implementation, using _log for logging
}

abstract class SomethingToDeriveFrom : SomethingAbstract
{
   protected ILogger Log { get; }

   protected SomethingToDeriveFrom()
   {
       Log = Log.ForContext(GetType());
   }
}

// Derived classes inherit from SomethingToDeriveFrom and use Log for logging