Lakshmi Narayan or Lakshmi-Narayana (Sanskrit: लक्ष्मी-नारायण, IAST: Lakṣmīnārāyaṇa), also sometimes spelled Lakshminarayan, Lakshminarayana, Laxminarayana, is a name of The Supreme Personality of Godhead in the Hindu religion. It is usually referring to Vishnu, also known as Narayan, when he is with his consort Lakshmi, in the causal ocean i.e. Karana Ocean, or it refers to the Narayana and Laxmi of Vaikuntha(spiritual world).
The deity Lakshminarayan has many historic roots and is sometimes interpreted by different traditions as for example Jayadeva, in his Gitagovinda, dealt with esoteric pastimes of Krishna with Radha, and identified Radha with Kamala, Lakshmi who appeared from the lotus who is regarded as the goddess of Love, Beauty, and Prosperity. the consort of Narayana. Jayadeva also regarded Jagannath as Krishna. Subhadra was treated as Lakshmi during the Ganga period, and afterwards. The Purushottama Mahatmya of Skanda Purana (13th century A.D.) and of Vishnurahasya (16th century A.D.) referred to the female wooden image between Jagannath and Balabhadra as Lakshmi.
In Swaminarayan Sampraday
In sect Swaminarayan Sampraday, the deity is referred to as Laxminarayan Dev. When Krishna - identified with Narayana in the text Shikshapatri - is with his wife Rukmini, a form of Lakshmi, he is also called LaxmiNarayan Dev. The founder of the sect, Swaminarayan installed the murtis of Laxminarayan Dev at the Shri Swaminarayan Mandir, Vadtal.
Lakshmi Naryana Frontispiece from the "Tula Ram" Bhagavata Purana - Brooklyn Museum