The "P" in ISRO's PSLV stands for "Polar".
Is there anything particularly "polar" about this launch vehicle, or is the use of the word in the name of the rocket more historical or for marketing purposes; i.e. "We don't need SDSC's ~0.45 km/s rotational kick to get you to space"?
Has the PSLV been used for non-polar launches? Are there any specific challenges that would have to be dealt with to put a payload in a low-inclination orbit instead?
From the beginning of the Wikipedia article that you linked in your question (bolds mine):
The Polar Satellite Launch Vehicle, commonly known by its abbreviation PSLV, is an expendable launch system developed and operated by the Indian Space Research Organisation (ISRO). It was developed to allow India to launch its Indian Remote Sensing (IRS) satellites into sun-synchronous orbits, a service that was, until the advent of the PSLV in 1993, commercially available only from Russia. PSLV can also launch small size satellites into geostationary transfer orbit (GTO).
Some notable payloads launched by PSLV include India's first lunar probe Chandrayaan-1, India's first interplanetary mission, Mars Orbiter Mission (Mangalyaan) and India's first space observatory, Astrosat.
All of the "notable payloads" listed in the second paragraph are in non-polar orbits (lunar and interplanetary launches generally launch to low or moderate inclinations; Astrosat is at 6º inclination). The name simply references the polar satellites it was initially developed to launch.
