The headword phrase comes from Diogenes Laertius 7.5, on the origins (with Zeno of Citium: zeta 79) of 'Stoic' philosophy: he would teach 'pacing up and down in the Painted Stoa, also [called] Peisianaktian but [named] after the painting of Polygnotus;' cf. sigma 1150, and Plutarch, Cimon 4.6.
For Polygnotus see generally pi 1948. On the Stoa Poikile (second quarter of the C5 BCE), in the Athenian Agora, cf. pi 3079, sigma 1126; see in brief OCD4 s.v.; more fully on its paintings Pollitt 141-5.
Peisianax is a rare name in Athens; LGPN ii s.v. lists only six, three of whom are too late to be of relevance here. Of the remaining three, one is the Peisianax somewhat shakily attested as a son of Kimon (kappa 1620, kappa 1621), the initiator of at least some of the Agora projects of the period (see Camp 66-77, 'Kimonian Athens'); but if the P. of the Stoa was the man who funded or otherwise facilitated it, we need an older man -- perhaps a brother-in-law of Cimon. (For this hypothesis see e.g. Davies 377-8.)