I read the word esplanade might not common anymore, so I would like to ask a synonym used commonly for it?
Can I name it as a coast-road, a road made by concrete or chemicals by sea that for only walking or cycling ?
Esplanade does have an old-fashioned ring to it, but only by association with old-fashioned seaside towns. if you happen to live in, or be visiting, an old-fashioned seaside town, it's a perfectly satisfactory word to use.
The word promenade seems about right:
A paved public walk, typically one along the seafront at a resort.
The word corniche could also be used, but the official definition doesn't quite fit:
A road cut into the edge of a cliff, especially one running along a coast.
The term coast-road is probably a bit too general: it could be applied to any road that runs along a coast. The one that immediately springs to mind would be route 101, which is definitely not just for walking or cycling.