Do not respond to the cease and desist notice before you understand your rights and explore your options and solutions. You do not want to unintentionally make any admissions that will weaken your position.
If you received a cease and desist from a competitor, you should take the notice very seriously. It is unlikely the competitor's threats will go away and if you wind up getting sued, it will cost a lot of money to defend it and you may be responsible for the other side's attorney fees.
You may have legal options that entitle you to use your trademark or business name. Also, there may be holes in the competitor's trademark that can be exposed.
Depending on the circumstances, there may be alternative solutions to explore, such as a co-existence settlement or a license agreement.