NO. Registration of Trademark means the owner has exclusive rights over the said wordmark/ logo/ slogan/ any other mark. Specifically, if the work mark is registered, you cannot use it even in other logo.
The trademark rights do not differ with popularity or scale of business. Law is same for all.
Also, you would always prefer a unique and original business name, specially unregistered one, because the trademark rights are based on first to use basis.
If you are looking for any professional assistance for online trademark registration, feel free to connect with LegalWiz.in experts.