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NGC 7581 may be NGC 7541. Dreyer credits the object to Holden, but it is not in either of the lists in the Washburn Observatory Publications that Dreyer credits in the NGC. Nor does Dreyer give a reference in the GC Supplement where the object first appears. If Holden published a note about the object, it must have been in the time between the GC's appearance in 1864 and the publication of the Supplement in 1878. Perhaps someone could check the appropriate journals of the time (AN, MN, The Observatory, AJ, and so forth).
In any event, the identity with NGC 7541 was first suggested by Reinmuth. From Die Nebel Herschel, it was picked up by Carlson, then RC1, and RNGC. The identity is reasonable: aside from being called "very faint," the remainder of the GC/NGC description "much extended, star 12-13 close following" is accurate. However, the position is 3 minutes of time off in RA, and 8 arcmin in Dec. These don't seem to suggest simple digit errors, though they could be.
I've put a question mark on the identification because of the position mismatch and the lack of a reference.
The RNGC (Sulentic and Tifft 1973) notes that this is a nonexistent object. Their coded description reads =7541 DC.
The Messier objects
The Bennett objects
The Caldwell list
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