The set-up:
1. Create a host group "A";
2. Create a template "T";
3. Assign template "T" to host group "A";
4. Create a host group "B";
5. Create a host "H";
6. Assign host "H" to host group "B";
7. Link template "T" to host "H";
8. Create a user group "G";
9. Set "Read-write" permissions to host group "A";
10. Set "Deny" permissions to host group "B";
11. Create a user "U";
12. Assign user "U" to group "G";
13a. Set "User type" to "Zabbix Admin" (for 4.0);
13b1. Create user role "R" and set "User type" to "Admin" (for 5.2 and higher);
13b2. Assign role "R" to user "U" (for 5.2 and higher);
14. Create host prototype on template "T";

The execution:
1. Log in with user "U" (regular admin);
2. Observe you have access to template "T", but not host "H" and there is a host prototype;
3. Change name and/or visible name of host prototype;
4. Observe it saves successfully;
5. Log in as Super admin and observe template host prototype on host "H";

Result:
The name and visible name (and other properties) as well remained the same.

Expected:
Name, visible name and other changeable properties should have changed, because they were changed on template.