Thank for you clarifying. You are correct, the service display name does not need to be unique. The only workaround to this problem I can think of would be to specify additional parameters such as the parent folder id. Though this is not as clean and easy to use if you do not have these ID's. It would also present the same issue if both services were under the same parent.
I will have to defer to the other communities members to weigh in here. Perhaps we can get some other suggestions to help you out.
/restman/1.0/services?name=Test&parentFolder.id=587179C7A8CB0A0A02937C64DCAD80F8
Regards,
Joe