Though I've never eaten at a Spires Family Restaurant, I do always notice them: I thought maybe the chain was founded by a very distant relative who forgot how to spell our name.
But no, the name seems to have been a fairly random choice by the founder, John Haretakis, who, by opening the first location in Anaheim, was carrying on the Greek American tradition of opening and running diners.
The west coast doesn't have nearly as many Greek-owned diners as the east coast, but we of course are familiar with the phenomenon. Some argue that Greek immigrants were rebuilding the kafeneion of their homeland when they perfected the American diner. This makes a certain amount of sense, as kafeneion are just as much community centers as coffee shops, and diners are famously a place where you can spend hours nursing a coffee without needing to spend more. (This article on the closing of a Long Beach Spires location focuses on the old-timers who came anywhere from a few times a week to twice a day; here's one about regulars' orders, tables, and parking spots.) On the other hand, many new immigrants open restaurants: it's a pretty classic all-American story.
Born in Crete, Greece's largest island, Haretakis moved to the U.S. in 1947 and first worked as a dishwasher. He put his L.A. spin on it by trying out acting first. He didn't have much success, but look at that headshot. The eyelashes! The brooding! Relatedly, here's a paper that discusses FDR requesting that Hollywood make movies depicting Americans and immigrants getting along, and how Greek Americans, previously looked down upon, had their reputation changed by Hollywood after Greek soldiers repelled Mussolini's army and screenwriters began depicting them as heroes - especially in the movie Haretakis was in, "The Glory Brigade."
Haretakis made the pivot to restaurant-owning in 1965, eventually expanding beyond Anaheim to 30-plus locations in Southern California and Texas. But, as these things go, the company has shrunk since its mid-'80s heyday. Today there are four locations, and (I think very tentative) plans for three more. They should dig up more of these weird old commercials and post them to socials — it would draw a younger crowd for sure.
More L.A. Restaurant History: