Hi Dan. Evidently they thought we'd never need to do that! Using the stock tools, it does not appear we can remove a name from a point. However, if you don't mind throwing a little bit of lisp at it, it can be done without deleting the point(s).
(defun c:jmm_resetpointnames (/ ss idx obj)
(vl-load-com)
(if (setq ss (ssget '((0 . "AECC_COGO_POINT"))))
(progn
(setq idx -1)
(while (setq ent (ssname ss (setq idx (1+ idx))))
(setq obj (vlax-ename->vla-object ent))
(vlax-put-property obj 'name "")
)
)
)
(princ)
)