I Have a requirement where i need to encrypt the "Account name" Standard Field. But my question is will it also encrypt the FirstName & LastName
Name consists of first name and last name. If you have Person Accounts enabled, Name = First Name & Middle Name & Last Name. First Name and Last Name (among other fields) are stored in a Contact record that is related to the Account record. You can use Account.PersonContactId to fetch the contact related to that person account to display First and Last Name.
When you encrypt any of the following Account or Contact fields, the equivalent fields in Person Accounts are also encrypted: Name, Description, Mailing Address, Phone, Fax, Mobile, Home Phone, Other Phone, Email (See https://help.salesforce.com/articleView?id=security_pe_considerations_general.htm&type=5)