No need necessarily to delete the mapping and redo it... you can edit an existing mapping, add properties, and change values from the name mapping page. But yes, the problem has to do with an inaccurate mapping criteria.
Letting TestComplete do the name mapping is a good start... but I would say something like 75% of the time, you need to edit what TestComplete maps to make sure that it's a unique mapping.
> you can edit an existing mapping [...]
https://support.smartbear.com/testcomplete/docs/testing-with/object-identification/name-mapping/managing/modifying/index.html for mode detailed description.
