Work on fixed installations (faste installationer) has to be done by an autoriseret elinstallatørvirksomhed (authorised electrical firm). Ask whether they hold the authorisation themselves or bring someone who does, and get that on the invoice.
Næstved is the hub of South Zealand, with a centre and nearby villages. A drive out of town is common. Ask whether the quote includes that drive. The same 4 businesses as the Danish page: 2ke-el ApS, BP EL-SERVICE ApS, Jespers El-Service ApS, TJ-ELservice A/S.