From BiblePortal Wikipedia

Hawker's Poor Man's Concordance And Dictionary [1]

This name is given to the church in the Songs of Solomon. ( Song of Song of Solomon 6:13) It hath been variously accounted for. Some have supposed that it is in consequence of her marriage with Solomon, and bearing therefore his name; for Shulamite is the feminine, as Solomon is the masculine, both being derived from Shalem peace. And if so there is a great beauty in it as it relates to Christ and his church; for if Jesus be the Shalem, the peace of his people, his spouse hath peace in him and his blood and righteousness. We have a beautiful instance of the same kind, and from the authority of the Holy Ghost,  Jeremiah 23:6 with  Jeremiah 33:16; where, in the first of these chapters, Jesus is called by JEHOVAH'S appointment the Lord our righteousness, and in the second the church, by the same authority, as one bearing the name of her husband, is called the same.

But beside these considerations there is a great propriety in calling the church Shulamite, for Shulem or Salem is the same as Jerusalem; and this is the mother of the church, ( Galatians 4:26) Hence Melchizedec is said to have been king of Salem, king of peace. ( Hebrews 7:2) What a sweet thought! Our Jesus, our Melchizedec, is king of Salem, and all his people are in this sense "Shulamites;" for they are "fellow-citizens with the saints, and of the household of God." ( Ephesians 2:19, etc.)

And it is very blessed yet farther to trace the propriety of the name in reference to the church's connection and interest with her Lord; for she is a Shulamite indeed in the peace and perfection of beauty put upon her by the comliness and perfection of Jesus. Hence when the daughters of Jerusalem, smitten with a view of her loveliness in Christ, call upon her, it is to return, that they may look upon her beauty. "Retrun, return, O Shulamite! return, return, that we may look upon thee." So struck were they with her righteousness in Jesus. ( Song of Song of Solomon 6:4)

Morrish Bible Dictionary [2]

Name introduced in the Canticles. It is a feminine noun traceable, like Solomon, to Shalom , 'peace.' It is the virgins who use this term. The union of the bridegroom and bride is such that she can be called by the same name. The 'two armies' seen in the Shulamite doubtless refer to the union of Judah and Israel.  Song of Solomon 6:13 .

American Tract Society Bible Dictionary [3]

Peaceful, in Hebrew a feminine name, corresponding to Solomon as Julia does to Julius. It is the figurative name of the bride in Solomon's Song, Song of  Song of Solomon 6:13; and the bridegroom is represented by Solomon , also meaning peaceful.

Easton's Bible Dictionary [4]

 Song of Solomon 6:13

Cyclopedia of Biblical, Theological and Ecclesiastical Literature [5]

(Heb. with the art. hash-Shulammith', הִשּׁוּלִמַּית , i.e. The Shulammitess ; Sept. Σουλαμυῖτις v.r. Σουμανεῖτις , etc.; Vulg. Sulamitis and Sunamitis ) , one of the personages in the poem of Solomon's Song, who, although named only in one passage ( Song of Solomon 6:13), is, according to most interpreters, the most prominent of all the characters, being no other than the bride herself. The name after the analogy of Shunammite denotes a woman belonging to a place called Shulem. The only place bearing that name of which we have any knowledge is Shunem itself, which, as far back as the 4th century, was so called (Euseb. Onomast. s.v.). On the theory that Shulammite and Shunammite are equivalent, some have supposed that the female in question who was the object of Solomon's passion was Abishag the most lovely girl of her day, and at the time of David's death one of the most prominent persons at the court of Jerusalem. This would be equally appropriate whether Solomon were himself the author of the Song or it were written by another person whose object was to personate him accurately. (See Solomon).

But this is abhorrent to the whole tenor of the Canticles, and is opposed to the Oriental usage with regard to the harem of a deceased king. (See Abishag).

It is far more reasonable to suppose that the title The Shulammitess was a poetical term applied to the bride in imitation of Solomon ' S name, as they are thus but masculine and feminine forms for "peaceful." (See Canticles).