Normally, our protein goals should not change markedly between when we are losing and when we are maintaining weight, as the goal in each case is to maintain our lean body (or muscle) mass, which (hopefully) won't change much as we lose the fat (there will inevitably be some loss, but we should try to minimize that with the typical protein recommendations and some strength oriented exercise.)
Once reaching goal weight, then one can evaluate their body composition (fat and lean mass amounts) and make adjustments accordingly, or if one wants to go into a muscle building program, then an increase may be in order.