I've always said and heard 'a change of plan'. Both 'change of plan' and 'change of plans' are correct. According to Google ngram viewer, 'change of plan' used to be more common and 'change of plans' has only recently overtaken it. Both are fixed phrases though, and you'd sound odd saying 'change of the plan'.

I live in New York state in the U.S., and it's most common to hear people say "change of plan" (singular). Sometimes I do hear "change of plans" (plural), but it's much less common, and it does sound a little weird to me. Both work technically, though: You can think of it as one all-encompassing plan, or you think of it as lots of little plans that get grouped together. But as others have said, both forms are fixed expressions, and both are correct.

"Change of plans" is a fixed expression. "Change of the plan" would sound strange to a native.

“Change of plan.” Also “there’s been a change in (or “to”) our plan (or “plans”).

‘Change of plan’ is the usual way of saying it here in England.