The headword, taken from the quotation which follows, is the present participle (nominative masculine singular) of the verb dhmosieu/w.
[1] The gloss on the headword which immediately follows has an accusative of respect (dwrea/n). But for simple transitive uses of dhmosieu/w itself see e.g. Xenophon, Hellenica 1.7.10 (to confiscate -- literally make public -- money), and generally LSJ s.v.I.1-4.
[2] Aristophanes, Acharnians 1030 (web address 1). This meaning is also attested in Plato, Gorgias 514D (web address 2).
[3] Excerpted from a scholion to the same verse (Scholia in Acharnenses - scholia vetera et recentiora Triclinii-, N.G. Wilson).
[4] The reading in the scholion (and in Codex Parisinus 2625, one of the manuscripts on which the Suda is based) is e)speisa/mhn, first person singular of the middle voice, instead of e)spei/samen, first person plural of the active. This is significant because, in addition to the change of person, there is a shift to the middle voice where the libation is clearly the metaphor of a treaty (as in Herodotus 3.144, Thucydides 4.99 and in this same work, at lines 199 and 1534). Therefore the sense of the phrase should be "I did not make a public treaty, but one just for me", which fits the context.