"Church" is a right translation; ekklesia simply means assembly, congregation, a synonym of synagogue. If Church is derived from the ancient "Lord's house", even then it has the same connotation as ekklesia or synagogue, since the assembly would only meet at a place, be it the official building or at a house, so it is going to conflate with the place of assembly.
Etymology of Church
From Middle English chirche, from Old English ċiriċe (“church”), from Proto-West Germanic *kirikā, an early borrowing of Ancient Greek κυριακόν (kuriakón), neuter form of κυριακός (kuriakós, “belonging to the lord”), from κύριος (kúrios, “ruler, lord”), from Proto-Indo-European *ḱewH- (“to swell, spread out, be strong, prevail”).
ἐκκλησία, ἐκκλεσιας, ἡ (from ἔκκλητος called out or forth, and this from ἐκκαλέω); properly, a gathering of citizens called out from their homes into some public place; an assembly; so used
- among the Greeks from Thucydides (cf. Herodotus 3, 142) down, an assembly of the people convened at the public place of council for the
purpose of deliberating: Act 19:39.
- in the Septuagint often equivalent to קָהָל, the assembly of the Israelites, Jdg 21:8 ; 1Ch 29:1, etc., especially when gathered for
sacred purposes, Deu 31:30 (Deu 32:1); Jos 8:35 (Jos 9:8), etc.; in
the N. T. thus in Act 7:38; Heb 2:12.
- any gathering or throng of men assembled by chance or tumultuously: Act 19:32; Act 19:41.
- in the Christian sense, a. an assembly of Christians gathered for worship: ἐν ἐκκλησία, in the religious meeting, 1Co 14:19; 1Co 14:35;
ἐν ταῖς ἐκκλησίαις, 1Co 14:34; συνέρχεσθαι ἐν ἐκκλησία, 1Co 11:18; cf.
Winer's Grammar, sec. 50, 4a.
On Synagogue: συναγωγή, συναγωγῆς, ἡ (συνάγω), the Septuagint for קָהָל and very often for עֵדָה. In Greek writings a bringing together, gathering (as of fruits), a contracting; an assembling together of men. (Τhayer)
συνα^γωγ-ή , ἡ,
A.a bringing together:
I. of persons, “ἀνδρὸς καὶ γυναικός” Pl.Tht.150a; collecting, ὄχλων, ἀνδρῶν, etc., Plb.4.7.6, D.L.2.129, etc.; “συμποσίου” Ath.5.192b; assembling, meeting, “τῶν λογιστῶν” IG12.91.9, cf. Test.Epict.4.7.
2. assembly, LXX Ex.12.3, OGI737.1 (Egypt, ii B.C.), etc.; “τῶν συνέδρων” IG5(1).1390.49 (Andania, i B.C.), cf. Test.Epict.4.25; place of assembly, esp. of the Jewish synagogue, Ev.Luc.8.41, Act.Ap.9.2, BCH 56.293 (Stobi), etc.; meeting-house, “Μαρκιωνιστῶν” OGI608.1 (Syria, iv A.D.); conventicle, Cod.Just.188.8.131.52.
συναγωγή (in origin abstract, a leading [bringing] together, convening an assembly, then concrete, a [religious] meeting), a meeting (assembly), a place of meeting (assembly), particularly of Jews for the reading of scripture and for worship, a synagogue. In certain passages it is doubtful whether the congregation (e.g. John 6:59. 18:20) or the place of meeting (e.g. James 2:2) is particularly intended, but the sense is not seriously affected by the doubt. In the O.T. συναγωγή and ἐκκλησία are practically synonymous, but in ordinary Christian writings the former is rarely used, and seemingly only of communities of Jews or Jewish Christians (e.g. James 2:2, where it is probably the building).
Souter, A. (1917). A Pocket Lexicon to the Greek New Testament (p. 246). Oxford: Clarendon Press.