To the best of my knowledge, only 18 minor planets have been named after their discoverers. While the discoverer has first naming rights, they cannot name a minor planet after themselves, though they can (and sometimes do) name a minor planet after a spouse, parent, or child.
Of course, many minor planet discoverers have minor planets named after them, but almost always these are discoveries by someone else who decides to name one of “their” minor planets after the other discoverer.
In the rare situation when someone decides (and has the authority) to name a discoverer’s minor planet after the discoverer, it is almost always a posthumous honor. Comet discoveries, on the other hand, are automatically named after their discoverer(s).
I have reader Rafael to thank for letting me know that Eugène Delporte does indeed have an asteroid he discovered named after him (see comments after Eugène Delporte and the Constellation Jigsaw) and this got me wondering if there were other examples. I wrote a SAS program to do some fuzzy matching between asteroid name and asteroid discoverer, and came up with the following list. Let me know if there are any others I missed, and I will include them here.
792 Metcalfia
Discovered 1907 Mar 20 by Joel Hastings Metcalf (1866-1925) at Taunton, Massachusetts.
989 Schwassmannia
Discovered 1922 Nov 18 by Arnold Schwassmann (1870-1964) at Bergedorf, Germany.
1074 Beljawskya
Discovered 1925 Jan 26 by Sergey Ivanovich Belyavskij (1883-1953) at Simeïs, Crimea.
1111 Reinmuthia
Discovered 1927 Feb 11 by Karl Reinmuth (1892-1979) at Heidelberg, Germany.
1274 Delportia
Discovered 1932 Nov 28 by Eugène J. Delporte (1882-1955) at Uccle, Belgium.
1596 Itzigsohn
Discovered 1951 Mar 8 by Miguel Itzigsohn (1908–1978) at La Plata, Argentina.
1648 Shajna
Discovered 1935 Sep 5 by Pelageya Fedorovna Shajn (1894-1956) at Simeïs, Crimea.
1655 Comas Solá
Discovered 1929 Nov 28 by José Comas Solá (1868-1937) at Barcelona, Spain.
1666 van Gent
Discovered 1930 Jul 22 by Hendrik van Gent (1899-1947) at Johannesburg, South Africa.
1777 Gehrels
Discovered 1960 Sep 24 by C. J. van Houten, I. van Houten-Groeneveld, and Tom Gehrels (1925-2011) at Palomar Mountain, California.
1927 Suvanto
Discovered 1936 Mar 18 by Rafael Suvanto (1909-1940) at Turku, Finland.
2044 Wirt
Discovered 1950 Nov 8 by Carl A. Wirtanen (1910-1990) at Mount Hamilton, California.
2246 Bowell
Discovered 1979 Dec 14 by Edward L. G. Bowell (1943-2023) at Anderson Mesa, Arizona.
3019 Kulin
Discovered 1940 Jan 7 by György Kulin (1905-1989) at Budapest, Hungary.
5540 Smirnova
Discovered 1971 Aug 30 by Tamara Mikhajlovna Smirnova (1935-2001) at Nauchnyj, Crimea.
5900 Jensen
Discovered 1986 Oct 3 by Poul B. Jensen (?-) at Brorfelde, Denmark.
19911 Rigaux
Discovered 1933 Mar 26 by Fernand Rigaux (1905-1962) at Uccle, Belgium.
96747 Crespodasilva
Discovered 1999 Aug 16 by Lucy d’Escoffier Crespo da Silva (1978-2000) at Westford, Massachusetts.
Incidentally, here are the three most prolific minor planet discoverers that still have an unnamed minor planet discovery that could be named after them. There are, of course, many others who deserve this honor.
Eleanor F. Helin (1932-2009)
Even though 3267 Glo is named after her nickname “Glo”, why not designate one of her discoveries as Helin or Eleanor Helin or Eleanorhelin? There are many still available, beginning with 5131 (1990 BG).
Carolyn Shoemaker (1929-2021)
Though 4446 Carolyn is named after her, why not designate one of her discoveries as Carolyn Shoemaker or Carolynshoemaker? There are many still available, beginning with 48576 (1994 NN2).
Gary Hug (1950-)
There are many still available, including 32165 (1998 FS92).