The story
Diachronically, from tel + Co., from the collocation of Tel. Co. as seen, for example, in Bell Tel. Co. or the names of countless local telephone exchange companies (e.g., Savannah Valley Tel. Co., Mutual Tel. Co., Tarrytown Tel. Co.), by abbreviation in the late 19th through mid-20th centuries; synchronically also a clipped compound as tel(ephone) + co(mpany).
Etymology from Wiktionary, CC BY-SA 4.0.