I'd love to be able to use some subject-affected form of ἐπινεύειν, but it that verb doesn't work syntactically as a subject-affected one. I like it because it expresses the subtlety of the host-guest relationship, and the expected body language that would have been part of the exchange if he had agreed to their request. Declining the invitation by not doing a small action is a lot less abrupt than our customary verbal mode of declining offers. Similar to the small incidental glimpses into the social conventions during the regency period that we read about in Jane Austin's description of the two balls, in reading this verse in Greek, we afford ourselves a glimpse into the politeness of the social interaction in the mid first century.
Acts 18:20 wrote:Ἐρωτώντων δὲ αὐτῶν ἐπὶ πλείονα χρόνον μεῖναι παρ’ αὐτοῖς, οὐκ ἐπένευσεν·
Perhaps though, acquiescing to the bestowal of wordhood might not be enough. If a stronger sense is implied, perhaps from the point of view of the decision, ἐπιτροπή ὀνομάτων might do, or from the point of view of the legitimacy of the word's use then κυριότης (II in LSJ) would be more appropriate.
I don't see how it could be all arranged together in one word like English (almost) can, because Greek words already have more morphed especially than English with their number-case etc. endings and prefixes.