The headword is either masculine accusative singular or neuter nominative/accusative singular of the adjective diw/numos, for which see also delta 1244. There, as also here, the adjective is used in the second of the senses registered by LSJ (web address 1). (For the first, see below.)
It is perhaps quoted here from Appian, who has four instances. See (e.g.) Syriaca 1.4 *)anni/ban [...] diw/numon e)pi\ strathgi/ais o)/nta, "[Antiochus lavishly welcomed] Hannibal on account of the great reputation he had earned with his military campaigns"; Civil War 4.7.54 kai\ *Sabo/rran, *)io/ba strathgo\n diw/numon "[Sittius also destroyed] Saburra, Juba's famous general"; 4.15.115 *domi/tios *kaloui/nos e)pi\ o(lka/dwn h)=gen o(plitw=n du/o te/lh *kai/sari, kai\ to\ diw/numon h)=n au)tw=n, to\ *)/areion, o(\ e)pi\ timh=| th=s a)lkh=s o)no/mazon "Domitius Calvinus was bringing two legions of infantry […]; of these [legions], the renowned one was the Martian, so called as an honor for its bravery". (On the fourth Arrian passage, see below.)
The Suda's glossing explains the adjective as derived from dia- and o)nom-. Compare, likewise, the instances in (e.g.) Plutarch, Timoleon 30; Josephus, Jewish War 5.1.3.
LSJ's sense I for the adjective (cf. epsiloniota 260; eta 544), is "provided with two (proper) names" or else "named together" (of two goddesses: Aeschylus, Phoenissae 683), related to a different etymology (di- "two" instead of dia-). Cf. ps.-Athanasius, Contra Arianos 4.9.2; "*)egw\ kai\ o( *path\r e(/n e)smen." *ta\ du/o e(\n ei)=nai/ fate, h)\ to\ e(\n diw/numon, h)\ pa/lin to\ e(\n ei)s du/o dih|rh=sqai; "'the Father and I are one thing'. That 'two are one' means either that the one has two names, or conversely that the one is divided into two parts"; Dionysius Thrax 9: diw/numon de/ e)stin o)no/mata du/o kaq' e(no\s kuri/ou tetagme/na, oi(=on *)ale/candros o( kai\ *pa/ris, ou)k a)nastre/fontos tou= lo/gou: ou) ga\r, ei)/ tis *)ale/candros, ou(=tos kai\ *pa/ris "'dionymos' means two names applied to one proper name, as Alexander is the one also called Paris, without the possibility of inverting the relation: for if one is called Alexandros, this same is not also called Paris"; 10 e)pw/numon de/ e)stin, o( kai\ diw/numon kalei=tai, to\ meq' e(te/rou kuri/ou kaq' e(no\s lego/menon, w(s *)enosi/xqwn o( *posei/dwn kai\ *foi=bos o( *)apo/llwn; "an eponymon is the name used along with another name to denote one subject, as Poseidon [is called] Enosichthon and Apollo [is called] Phoebus". In the same way the word diwnumi/a is used by Herodian, De figuris 103.11, in reference to the Homeric instances of Scamander and Batieia; cf. scholia on Homer, Iliad 1.403, 15.336 (Eriopis-Alkimache), 20.40b2, 20.73-74; Odyssey 5.334 (Ino/Leukothea); scholion on Pindar, Olympian 9, 79d (Deucalion/Opountes; Arnaea/Penelopes); Pythian 3.177b.
"Term with a double meaning" is the sense of diw/numos in kappa 151, q.v.
A scholion on Homer, Odyssey 12.22 attests the form disw/numos as an equivalent of diw/numos. With this meaning may be related Appian, Iberica 15.98 th\n do/can h(gou/menos diw/numon e)pi\ tou\s mega/lois gi/gnesqai kakoi=s, "[Scipio destroyed Numantia] as some think, in order to acquire the glory of two surnames from two great calamities" (tr. H. White).