The general term is solderable magnet wire. Magnet wire comes with many types of insulation. Some insulations are solderable (heat from soldering iron will melt the insulation), some require mechanical stripping/abrading or chemical stripping.
A common solderable magnet wire is PN (Polyurethane-Nylon insulation material), however, there are other solderable types of insulation available like polyurethane and polyester. The insulation is also classed in to thickness of the insulation, single, double (heavy), triple, & quadruple build.
I normally use HPN-155 (H: heavy insulation which is a double coat; PN: polyurethane-nylon insulation, 155: 155°C temperature class) for winding transformers and inductors.
Polyimide (240°C class) and enamel insulation requires mechanical abrading or chemical stripping, so I would avoid those types of insulation.
CAUTION Solderable Enamel Wire emits toxic vapour when soldered. Ventilate area well.– Chester Gillon Jan 10 '24 at 19:55