Can a Salesforce.com FIELD NAME be changed inside of a Salesforce Table?

NOT a FIELD LABEL. Can an existing default field name be renamed or do I have to create a custom field only...?

I ask because I need to change the TASK Table in Salesforce but there is no way to add a new Custom Field in the TASK Table in the Object Manager. See image.

Note the NEW custom field button is not available
If there is a way to do this please tell me how? Thank you.

Here in another table you can see a NEW custom field button is available. My problem is it looks like I am going to need to change the types and or names of some of the fields in the TAST Table in order for it to work.

New Button is available under CONTACT Table....Why not the TASK
RUA Volunteer2?Tableau Trainer & Consultant Sales Exec.Asked:
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RUA Volunteer2?Tableau Trainer & Consultant Sales Exec.Author Commented:
Answering my own question. Since I have access to the Salesforce support portal. Shows me this link.

https://success.salesforce.com/answers?feedtype=RECENT&criteria=BESTANSWERS#!/feedtype=SINGLE_QUESTION_SEARCH_RESULT&id=90630000000gjGHAAY

The meat of the conversation is stated by the following.

Best Answer chosen by Miglena (Salesforce.com)
Steve MolisSteve Molis
 You need to create them on the Activity object, Tasks and Events are types of Activities. RUAVOL2 edit. Create them in the ACTIVITY TABLE.
May 21, 2011

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