It is a fine couple of questions, but there can be understood to have a wide array and degree of answers from the more purist absolute of saying the course looses the personal as soon as a committee or board begin the oversight of maintenance and grounds and make any change (which may happen pretty soon after the archie leaves it behiind). Or, it can be very vague with many changes in maintenance, from mowing and cultural habits to changes in turf species and shapes and technique of maintaining bunkers.
In my mind, it can remain a personal identity if it is and has always been a source of club or ownership pride that so-and-so archie designed the golf course, and if he or a specific construction entity are also part of the provenance cited to identify the course by quality of design and desirablilty or popularity of playing the archies finished product. I think a golf course can and most any architec will acknowledge must undergo change, evolution, or tweaking. All archies know the effect of time, erosion from drainage or wind, hot or wet and varied weather conditions, funds or economy to maintain, and of course ever changing B&I techology will beckon those in charge to respond and make that wide array and degree of changes. Obviously, some changes would not be with approval or support from the original archie.
But take a course like Crooked Stick or Pinehurst #2, or others where the original archie himself has undertaken many changes. Do you say that archie took the personal from his own version of early years and youth? Would you say by means of identification, it is a Donald Ross the younger, or an older Donald Ross design?
When a successor archie comes around and changes the routing, changes the bunker placements, changes the slopes and grades in FWs and greens, to any extent, either a single hole, part of the course or all of it, I think the credit or blame has to be stated when the course is referred to as a specific architects product. The course should be referred to as a Donald Ross original, but or also a Ron Prichert (insert appropriate name) remodel of x y or z aspect of what was altered.
I think the GCA.com group generally do right and are more diligent to speak of various significant courses by known architects, and often when speaking of the course qualities, note (if known by the GCA poster) other archies or committees input that notably changed that original archies work and vision.
But, when the collective and oversight of a particular golf course/club starts fudging the truth and stating a course is designed by someone with name prestige but they as a collective have changed it away from what the archie would claim as his, then that is deception in advertising or fraud in prestige, IMHO.