You're not the first person to wonder about this. In his book The Spirit that Gives Life: The History of Duquesne University, Joseph Rishel quotes a local ditty that once noted, "No one knows the reason, no one can explain / but everything you look at is named Duquesne."
And you're right: Despite spending most of the 1750s in North America, Ange Duquesne de Menneville never did set foot here. Then again, neither did William Pitt. Given the city's later population losses, maybe it's ominous that its earliest names belonged to people who never visited. But both names were given by military men caught up in a triumphant spirit.
Prior to Duquesne's 1752 arrival in the New World, the French carried out what might be the most laid-back invasion in history: They asserted their claim to the region by burying lead plates all over the place. The plates were inscribed with messages like the following: "[T]o reestablish tranquility in certain Indian villages [we] have buried this plate ... as a monument of renewal of possession which we have taken of the [Ohio River] and all its tributaries, and all the land on both sides, as far as the sources of the said rivers."
Calming a native populace, asserting territorial dominance over whole regions ... maybe we should be planting plates in Iraq.
On the other hand, Native Americans had been burying things for generations, yet nobody ever seemed to respect their land claims. And as George Fleming's History of Pittsburgh and Environs observes, burying plates "as a means of taking possession of new territory ... was peculiar to the French in North America."
In any case, the crockery somehow failed to dissuade British plans for expanding westward into the American continent. And the Marquis Duquesne decided a more assertive approach was necessary. He launched a much larger campaign throughout Western Pennsylvania -- this time to construct a string of forts (above ground, where people could see them) from Erie down to Pittsburgh.
Duquesne's strategy was not popular; many officers felt he was devoting too many resources to too small an area. But when the French reached the Point and captured a crude English fort -- a conquest made easy because the commander wasn't at home -- Duquesne touted his success.
"The English have withdrawn, looking foolish, and in less than an hour's time [we] have become master of the battlefield," went Duquesne's boasts as quoted in Laura L. Frey's history The Land in the Fork.
The commanding officer on the scene, Pierre de Contrecoeur, decided to build a larger fort, and since it was the climax of Duquesne's campaign, he named it after the governor-general. (It could have been worse: Another French fort, built south of Erie, was called "Le Boeuf" -- "the ox." Although come to think of it, that might have made a more fitting name for an old boy's club ...)
In 1758, continuing the game of Freudian one-upmanship, the English captured the fort and built an even bigger one, called Fort Pitt.
But for a variety of reasons, the French name was harder to dislodge than the French themselves.
In the case of Duquesne University, Rishel notes that Duquesne was originally called the "University of the Holy Ghost." But there were fears of associating "the sacred name of the 'Holy Ghost' with the mundane world." (You can see the confusion that might result from newspaper headlines like "Cash-strapped city seeks money from Holy Ghost.") So eventually, "Duquesne" was proposed as a "more distinctive name which will indicate the locality in which the [school] is situated."
The university had a special incentive for its choice: The French were, after all, largely Catholic. But as Rishel suggests, "Duquesne" had non-sectarian advantages too: It's local and distinctive. Plus, French words are classy-sounding: Just ask the Duquesne Club, or the suburban Sun Kings in North Versailles. And as for a place like Duquesne Brewery, what other choice did it have? By the time it started in 1899, "Iron City" was already taken.
Fort Duquesne lasted half a decade, but French names have remained planted in the local soil for 250 years. Maybe burying plates was the right idea after all.