Another line of thought for discussion: In Thomas Hogg's 1823 "A Practical Treatise on the Culture of Carnation, Pink, Auricula..." on p. 208 are listed following hyacinths (full text of 1839 Edition can be found):
Rex rubrorum
Rose agréable
Rose d'Ispahan
All of these names are listed by Sweet in 1827 and Don in 1832 as names of garden roses. There may be more.

I have a hunch that Sweet resp. Don just ballooned their listings with names they found published somewhere. These names are not found in contemporary French catalogues. Later in 1842 /1849 Bosse mentions these as Centifolia or Gallicas and gives colour descriptions. Others repeat and hey presto! we have a centifolia 'Ispahan'.

In the German Newsletter "Allgemeiner anzeiger" of 1824 is a description of the rose-coloured double hyacinth:
Rose d'Ispahan, with dark stripes, very double, multi-bells, perfect.

I've read that the book, 'Rosen - die große Enzyklopädie,' states that it was brought to England by Norah Lindsay, but don't have that book, can't vouch for its alleged contents, and wonder about it giving credit to the wrong Lindsay. Google Books informs me that GST mentions it as Ispahan, Rose d'Isfahan, and Pompon des Princes on p. 157 of 'The Old Shrub Roses' (1955), but I gather that no origin is specified there. Since he credits Nancy Lindsay when mentioning Rose de Rescht, Gloire de Guilan, etc., I'd wonder at his not mentioning her in relation to Ispahan.
<edited to update>
Pages 143-8 of GST's 'Cuttings from My Garden Notebook' have much to say about Nancy Lindsay and her roses, and the relevant points I noticed were:
She felt at perfect liberty to name found roses which she could not identify, though all but a few were later identified by others as already known and named cultivars. (I just added a comment at 'Empress Josephine' giving GST's main quote on the subject.)

She was very jealous and protective of her roses, and flew into a rage when she discovered that GST had obtained budwood of them from Kew, as she had let Kew have them only because she had been unable to care for them for a while, and believed she had an agreement that Kew would not share them with anyone. While she didn't feel too strongly about garden cultivars she found in cities, like Rose de Rescht and Gloire de Guilan, she was livid that Rose d'Hivers had been shared. She said that she'd risked her life in the wilds of Persia to get it, and considered it her very personal baby. She also did not consider its name to be final; she said that before Kew shared it, "I ought to have had stock of it first, and had it named and shown it myself... I'd always hoped that my rose would be named after me..." In her rant against Kew, she says she'd agreed "that none would be passed on until they had been named, shown and recorded and I'd given my permission." (GST consequently removed Rose d'Hivers from commerce, and unless Kew still has Sharastanek, her jealous guarding of her roses may have resulted in its extinction.)

All this leads me to believe that the names attached to NL 292 'Ispahan,' NL 465 'Sharastanek,' NL 849 'Rose de Rescht,' NL 1001 'Gloire de Guilan,' and NL 1409 'Rose d'Hivers' were tentative working names. Apparently Rose d'Hivers was supposed to be named 'Nancy Lindsay,' so 'Pompon des Princes' may have been what she finally chose for NL 292. Other than 'Sharastanek,' whose etymology escapes me, all of the names first used are descriptive, i.e., named after the city or province where they were found, or from the fact that Rose d'Hivers was dried for use in winter. I suspect that what we now know as Ispahan may not have had that name (or Pompon des Princes) before the 1940s, and while 'Mogul Temple Rose of Persia' points to the country of origin, I'm left wondering what it was called in Farsi or Arabic before Lindsay collected it and stuck her tag on it. Alas that we seem to have no Iranian rosarians here.