Come into (one's) own phrase
If a person "comes into his/her own", he/she becomes fulfilled, successful, or reaches a stage of maturity.
Dan has come into his own for a couple of years as one of the most successful actors.
Lily fully came into her own when she got accepted to an multinational corporation.
If something "comes into its own", it becomes useful in a particular situation.
Bring your umbrella, it will come into its own when the rain falls.
The verb "come" should be conjugated according to its tense.
"One's own" is a traditional ellipsis for "one's own property/estate" (as in the 17th-century English song written during the Cromwellian interregnum, titled "When the King enjoys his own again".