It depends on what you are using to consume the service and how you want to use the services. If you are using ArcGiS Online (AGOL) or Portal then no, this is not possible because the request to the server hosting the service is coming from the server hosting the web-application (Portal or AGOL). You can add a secure service to AGOL or Portal and store the username and password and use the limit usage tool. But the domain and IP restrictions that you can put in place are relative to the server hosting the web application not a users machine. ESRI wants named users/groups to be used to implement service level restrictions. And if the user is viewing the map in AGOL or Portal then they are logged in and therefore they fall under the username/group security umbrella in which case you can restrict access.
If you are trying to restrict access on the service level to a specific users then you could use a reverse proxy. If you are using Web adaptor you can place the reverse proxy in front of the WA. But this has limited value because in most cases (99.999%) a service is not very useful until it is added to some mapping application and once that occurs it is the apllications domain/IP making the requests for a service not a user.
Basically we are stuck with named users or restricting access to services based on the mapping-application.