You can do something like this:
string headerSpecific = "Specific";
string headerAll = "All";
var query =
specificPersons.GroupBy(_ => headerSpecific )
.Union(
allPersons.GroupBy(_ => headerAll));
Note you have other ways to accomplish similar functionality (although not matching your question's requirements), for instance using anonymous types instead of groups:
var query =
specificPersons.Select(p => new { Header = headerSpecific, p})
.Union(
allPersons.Select(p => new { Header = headerAll, p}));