Barbara Walters never expected a role in the renaming of Avery Fisher Hall. But it turns out that Ms. Walters, the ABC News broadcaster, was a crucial go-between who helped engineer a relationship between two of her friends that led to the unlikely, seemingly overnight emergence of the West Coast mogul David Geffen as one of New York’s most prominent philanthropists.

“You could say I was the matchmaker,” Ms. Walters said.

Just three weeks after a surprising announcement that finally marked progress in long-delayed efforts to overhaul the hall, the outdated home of the New York Philharmonic, the back story of how Mr. Geffen’s $100 million gift came about is surfacing, as are questions about the gift’s size and terms.

No one in the world of cultural philanthropy disputes Mr. Geffen’s generosity. But some ask whether his gift is large enough to warrant the renaming of such a prominent building, given that it represents just 20 percent of the projected renovation cost.

There are also lingering concerns about how much New York City will contribute to the project and whether Lincoln Center’s promise to never remove Mr. Geffen’s name from the building was shortsighted.