Currently there's no way to rename SLAs in Service Desk. However, this can be achieved via direct database modification.
This example explains how to rename an SLA from SLA1 to SLA2 in a Service Desk with project key SD.
Step-by-step guide
Direct database modification is not supported. Please make sure to back up your database or create an XML backup in JIRA before attempting this workaround.
Identify the ID of the SLA custom field (notice the use of SLA1 as the name of the SLA custom field):
select ID, cfname from customfield where customfieldtypekey like '%sla%' and cfname = 'SLA1';
By default, this custom field is Locked and has the same name as the SLA
Identify the ID of the Service Desk (notice the use of SD as the project key of the Service Desk):
select ID from ao_54307e_servicedesk where project_id = (select ID from project where pkey = 'SD');
As the same SLA can be used in multiple Service Desks, it's good to make sure that you only change its name where necessary
Identify the SLA itself:
select ID, name from ao_54307e_timemetric where custom_field_id = <ID_from_query_1> and service_desk_id = <ID_from_query_2>;
It should have the same name as the SLA custom field, which is SLA1 in this case
Once you're sure this is the SLA you'd like to rename, rename it (notice the use of SLA2 as the new name):
update ao_54307e_timemetric set name = 'SLA2' where ID = <ID_from_query_3>;
This doesn't require a JIRA restart - you can just refresh your SLA page and the SLA should have been renamed successfully