Sharing a City Apartment With a Big Dog? Good Luck.

When Diana Rhoten walks her dog, DZA, in Manhattan, she knows to expect people to comment.

“Oh, you’ve got a horse,” they tell her. “Can I put a saddle on that thing?”

DZA, which is pronounced DIZZ-uh and stands for Doggo Zig-Zag-Zig Allah, is a 156-pound Great Dane named for the rapper RZA, of the group Wu-Tang Clan. Like an exceptionally tall person fielding inquiries about the weather “up there,” he is a frequent target of snarky remarks.

But DZA, Ms. Rhoten said, is a good-natured beast who doesn’t yap, chew shoes or run in circles like many of the small dogs living in New York City apartments. He really wants nothing more than to sit in her lap.

The managing director of Purpose Venture Group, a strategic advisory firm focused on climate and social impact, Ms. Rhoten, 56, has learned the hard way that the perception of big dogs, accurate or not, influences the reality of urban real estate. Five years ago, when she and her husband, the journalist John Heilemann, were apartment hunting with their two Great Danes (the elder, Phife Dog, has since died), they were rejected by 27 landlords. Eventually, they gave up and bought a unit in the TriBeCa building where they were living and where the dogs were known quantities.

Now the couple are thinking about going back on the housing market with DZA. Will the prospective buildings impose a weight limit, as they often do? Will Great Danes be on a list of forbidden breeds, as they frequently are? Will the management charge a monthly pet rent that can be as high as $100? Will it insist on meeting DZA, and if so, will there be chemistry?