Learn English – word for a picture of a face that is made from the letters of a name

You can call them abecedarian words.

Abecedarian is an adjective meaning "being arranged alphabetically". It comes from the Latin abecedarius, which means "alphabetical," based on the names of the first letters of the Latin alphabet.

For example, below are the terms mentioned in a personal site:

Abecedarian Words: Words with letters in alphabetical order
Strictly Abecedarian Words: Words with letters in alphabetical order without repetitions

_{http://www.tanyakhovanova.com/}

It is also mentioned in this stackoverflow question:
Counting abecedarian words in a list: Python

carefree

ADJECTIVE
Free from anxiety or responsibility.
‘the carefree days of summer’ Lexico

carefreeness

The trait of being without worry or responsibility vocabulary.com

But for most of us carefree living is taking no responsibilities and an escape from the world itself. ref.

Childhood is idealized as a carefree period—no responsibilities, no worries about calories. ref.

She had been eighteen, no age at all really, but though they had both been delighted at the thought of parenthood, carefreeness had flown out the window. ref.

You could refer to a carefree state/existence, or the state/condition of being carefree if that works better than carefreeness.