I have a polylines shpfile that consist multiple parts - a water supply network. One part should be one record in att table with name - but, unfortunately, it's made up of a dozen short sections. Ideally, they should be combined into one layer and name of this one part should be "uploaded" from points shapefile. Shapefile (points) lays over the polylines contain name of part. How to combine them so finally it will one polyline shapefile where one record contain name.
I would suggest using a spatial join to give the intersecting or nearby polyline the correct record name, based on the point layer. If these polylines have a common attribute (e.g. the record name based on the spatial join), you can use the dissolve tool to turn the polylines into one record. Merging these polylines may require some manual editing. Here is an Esri page on merging features in the same layer.