The historic mansions on Hillhouse Avenue, which Charles Dickens once famously described as the “most beautiful street in America,” are full of character — but many of their names are not.

Only 10 of the 23 buildings on the two-block street, which is home to various academic departments, the School of Management and administrators’ houses, have names, while the rest are known by their addresses. These nameless treasures include the Yale Collection of Musical Instruments, “15 Hillhouse,” and the department of anthropology, “51 Hillhouse.” But as these buildings age and require renovation, University President Richard Levin said Yale may seek gifts to support their restoration, and naming them for donors in the process.

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“When we renovate, it would be a great time to interest a donor to name [the building] in recognition,” Vice President for Development Inge Reichenbach said.

Because rehabilitating the grand buildings is costly, Levin said administrators prefer tying the projects to significant gifts, and this often leads to the renaming of the building.

In 2003, when the University wanted to move the Provost’s Office to a new location, Levin said administrators identified 1 Hillhouse as a good candidate. After seeking a donation to anchor the construction, administrators landed the support of Douglas A. Warner, Jr. ’41, Douglas A. Warner III ’68 and Michael D. Warner ’04 to support the project. The building is now named “Warner House.”

“Programmatic need drove the solicitation of a gift,” Levin said.

A similar fundraising drive occurred in 2001 to support the renovation of 31 Hillhouse, which houses the Ethics, Politics and Economics and International Security Studies programs, and is now called “Allwin Hall.”

The renovation of 1 Hillhouse was the last time that the University renamed a building on the street, said Lesley Baier, senior editor in the office of the University Printer. Baier’s office is responsible for crafting the blue signs that identify buildings on campus by name and address.

Levin said it may be some time before any additional buildings on Hillhouse Avenue are named for donors. Because the University froze construction in the wake of the financial crisis that struck in 2008, Levin said renovating buildings is not at the top of administrators’ list of priorities.

Still, there will likely be many opportunities for donors to name a mansion in the future.

Since the Hillhouse mansions were built in the mid- to late 19th century, some are in need of repair. Benjamin Polak, chair of the economics department, said in an e-mail that the department’s home at 28 Hillhouse could use a “facelift.” Although the building received scheduled repairs last year, Polak said further renovations would improve upon its current condition.

“Given unlimited funds, one could do some great things in there,” Polak said. “For example, the third floor — the old servants’ quarters — is very dark. It would be great to let light come in from the stairwells as was the original design.”

But the upgrade is not urgent, Polak said, describing 28 Hillhouse as “a beautiful old building.”

Levin, for one, said he would welcome renovations in an old hangout of his — the offices in 28 Hillhouse that he once occupied as an economics professor and department chair.

“I’d be happy to name 28 Hillhouse one day too,” Levin said. “I’ve spent much of my career in that building.”

Reichenbach added that she would likely look for donors with ties to the specific buildings, for example, an economics major to contribute to the restoration of 28 Hillhouse.

Some of the street’s buildings currently belong to the School of Management, but will be in new hands when that school moves to its new facility on Whitney Avenue in 2013. Reichenbach said the subsequent renovation of the School of Management’s former buildings will provide a further opportunity for donors to leave their names on Yale’s campus.

The School of Management’s new home will be named for Edward P. Evans ’64, the donor who pledged a $50 million gift to the school in December.