Common phrase for "intermediate goal"

If by interim goals you mean goals along the way, short of the ultimate goal, then such often are called milestones. Wiktionary shows two senses either directly or figuratively applicable:

A stone milepost (or by extension in other materials), one of a series of numbered markers placed along a road at regular intervals, typically at the side of the road or in a median.
An important event in a person's life or career, in the history of a nation, in the life of some project etc.

Also consider the terms waymark ("A sign or symbol marked in a prominent position in an off-road location to show the track of a footpath or route") and benchmark ("A standard by which something is evaluated or measured") and synonyms including landmark and signpost.

The terminology mentioned above is less applicable in a mathematical context. There, consider terms such as lemma ("A proposition proved or accepted for immediate use in the proof of some other proposition"), or for arithmetic, subtotal.

The process of setting goals is called planning or might be referred to as scoping.

In British English the term waypoint would often be used in this context, being derived from navigation i.e. a staging point towards the final destination.

A checkpoint is "a point where a check is performed" or "a point or item, especially in a procedure, for notation, inspection, or confirmation." It is used as a point where the forward progress of something is temporarily suspended to evaluate the status or condition of the situation before allowing it to proceed once again. It is definitely an interim point, not the finish line. (For example, many of my children's teachers used the term checkpoint in a long-term project for the point when a rough draft of something was due.)