When a global text search is performed on a table, the search does not look into related records, so not extending to related lists within a main record.
This is working as expected and by design of the platform, global text search does not search through related lists.
When a text search is running on a certain table, in order for the searched term to be retrieved and returned in the results set, this needs to be present in one of the following places:
1. Record's XML (as a field value)
2. Record's Attachment
3. Record's Journal History/Activity Stream
4. Record's Variable
For example, if a CMDB record in a related list, such as a CI Name, is wanted to be returned from a search on a task table, such as Change Request, the wanted CMDB element should be mentioned within the activity log of the change request, so that it meets the 3rd criteria above and the change request record will be returned from the search.
For additional information, please consult the global text search doc pages: