In theory, it is the buyer who has the right to choose the notario they want to work with. If you work through Realty San Miguel, we have notarios that we recommend and prefer to use. 

However, sometimes sellers who will be subject to substantial capital gains taxes "shop around" their sale to various notarios until they find one that gives them the most favorable tax results. When this is the case, a seller may specify that they want to use a specific notario when the house is being shown. Sometimes, this issue doesn't come up until they are negotiating an offer. 

Bottom line: although technically speaking the buyer chooses the notario, it is not uncommon that the choice of notario becomes a point of negotiation between the buyer and the seller.