The nuance of the imperfect ἐκάλουν in Luke 1:59 is debated.
Bock (166) suggests it is a “conative imperfect” (that the crowd were wishing/wanting to name the child John).
Nolland doesn’t comment on the imperfect itself, but translates it as “wanting to call him” (77).
Culy, Parsons and Stigall claim “it is much more likely that the imperfect portrays what they were actually doing before Elizabeth corrected them” (50). Hence their translation is “began to call him…” (47).
The reasoning for Culy et als. interpretation is difficult to justify. They claim that “[c]onjoining on imperfect active verb to an aorist active verb that has the same subject using καί…appears to be a common means of pointing to…the onset of an event that is portrayed as a process…”. Their claim is that the aorist ἤκουσαν of v58 provides the necessary aorist for this interpretation to be valid.
However, there is a great deal of space, a number of phrases and a καί ἐγένετο ἐν clause inbetween these two verbs; and it is simply not true that these two verbs are conjoined. All of which make this interpretation unlikely
[ It is possibly that the authors were actually intending to refer to the ἦλθον of v59. This is an aorist, has the same subject and is καί-conjoined to the imperfect. This would make a great deal more sense! ]
Of these two options, a conative is more likely.
Further weight for this interpretation is given by the fact that in its usage here, καλέω has a telic sense (“to name, provide with a name” (BDAG 1 c, p502)). A telic verb coupled with the imperfective aspect of an imperfect tense-form produces a conative sense, i.e. an action which is intended but never completed (“they were attempting to name him…”).