What was the solar system called before the discovery of the heliocentric model? For that matter, was it difficult for the phrase "solar system" (or the equivalent in other languages) to take off, given clerical opposition to the theory?

Until the laws of planetary motion were established, no one knew for sure that the local planets were a system at all. That was kind of the point of them!

The "clerical opposition" is an odd idea In reality, the church commissioned, funded and published pretty much all the work on the subject. Including galileo. His work wasn't published because it failed peer review, not for theological reasons. Galileo's mathematical model didn't work, his observations were incomplete and his work was full of outright fiction which he refused to be corrected on, like his idea that the tides were caused by the earth's rotation even though there are two tides a day and only one rotation. That's why they asked him to stop promoting and teaching his work. He refused, abused the Pope and got jailed.

As soon as kepler corrected the models and matched them to observations, the church accepted and published the work. That would be a bit strange if they were opposed to heliocentrism, wouldn't it?