What to call a group of people in the society which are all single (meaning not being in relationship). Singles?
Singles is a common word for this:
https://www.merriam-webster.com/dictionary/single (first noun definition)
Single people also works just fine.
I hear the term singles a lot when talking about events designed for single people to attend, such as a Friday Singles Mixer, but it works in any context.
I invited my friend out dancing on Friday. It's just for singles, so hopefully we'll meet some great people!
Note that it's uncommon to call just one person "a single", but when referring to a group of single people, calling them "singles" collectively is correct. When referring to one person, you'd use the adjective single ("he is single", "I am single", etc).
You could refer to them as unattached.
adjective: not married or not having a relationship with anyone; single
You could call them "unattached people".
In my experience, you would also be understood if you used it as a noun in the same way you would use "singles". As in...
I have started a dating service targeted at the unattached.
Definition of singleton
1 : a card that is the only one of its suit originally dealt to a player
2a : an individual member or thing distinct from others grouped with it
b : an offspring born singly "singletons are more common than twins"
further source and examples:
1.2 informal A person who is not married or in a long-term relationship.
‘At tonight's game there don't seem to be any singletons on the prowl, but there are three couples on the ice.’
‘And 1.95 million single women live in New York City - the Mecca of singletons - alone.’
‘Her job is so much fun, she said, and time-consuming, too, that she has postponed ending her days as a singleton, also fodder for the cynicism and suspicion of others.’
‘This totally non-profit venture will bring singletons together for a night of frivolity.’
Word forms: plural singletons countable noun A singleton is someone who is neither married nor in a long-term relationship.
Bank is a 38-year-old singleton who grew up in Philadelphia.