Rule or sovereign power
Reighn is a modern creative spelling of the English word 'reign,' which refers to the period during which a sovereign rules. It is part of a contemporary trend of using word-names associated with royalty and power, often modified with unique spelling to distinguish it from the common noun.
Less common today
Reighn isn't in the latest US Top 1000. It last peaked at #4,785 in 2022.
US births per 5-year period, 1990βpresent (SSA data).