No, $MATIC is not automatically swapped to $POL.
Polygon ($MATIC) and $POL (Polygon 2.0's proposed token) are part of the Polygon ecosystem, but they are distinct tokens. The transition from to $POL is part of Polygon's broader upgrade to Polygon 2.0. Token holders will likely need to manually swap their tokens for $POL when the process becomes available.
Polygon has indicated that they will provide a migration path for $MATIC holders to convert to $POL, but it won't be an automatic process. Keep an eye on official Polygon announcements for detailed instructions on how to proceed when the swap process is live $MATIC