...
For custom field types which represent picklist value/s (Combo Box, Checkbox Group, Radio Group and Multi Select) things are slightly different. When you GET the resource you the Id and Text of the picklist value is returned. (To get a list of valid picklist values for the custom field you can use the customfield/{name}?$expand=Options resource.)
...
When you PUT picklist values - only the Id is required. This is the Id of the pick list value. The list of Ids for picklist values can be retrieved via the customfield/{name}?$expand=Options resource.
Here's a an example:
Get the list of Picklist Value Ids
...