Was this right after Rechav'am died?
Rashi: It was the next year 1 .
Radak: Perhaps it was. Rechav'am entered his 18th year, but did not complete it, therefore the verse says that he was king only for 17 years.
Why is he called Aviyah in Divrei ha'Yamim II, e.g. 12:16?
Malbim: Also Yaravam had a son named Aviyah. Yehudah called Rechav'am's son Aviyam; the suffix Mem is a pronoun, i.e. their Aviyah. Also, it was to distinguish him from Yaravam's son.
QUESTIONS ON RASHI
Rashi writes that this was the year after Rechav'am died. Why did Aviyam delay before becoming king?
Radak: Perhaps (he became king immediately); Rechav'am entered his 18th year, but did not complete it, therefore the verse says that he was king only for 17 years.