Is there more than one Joseph in the Bible?

Yes, there are more than one Joseph in Scripture. There are at least three distinct men named Joseph in Scripture.

In Genesis is Joseph the Patriarch, who was sold into slavery by his brothers, and who eventually rose to a position of great power in Egypt.

In the new testament, we read of Joseph, who is Mary's husband (Mary being the mother of Jesus) as well as Joseph of Arimathea.

There is more than one person named Joseph in the Bible.

The first Joseph that figures prominently in the biblical narrative appears in Genesis. Joseph is a son of Jacob, who is Israel. God spoke to Joseph in a dream, which showed that his brothers would one day bow down to him. Joseph is sold by his ten older brothers into slavery as a boy. Joseph is taken to Egypt, and later becomes very powerful there. His brothers were filled with jealousy because Jacob favored him and his younger brother Benjamin because Jacob loved their mother, who was not the same as the mothers of his brothers. Joseph's dream comes true, and Joseph is able to redeem his brothers by saving them and their families from a great famine. It was by Joseph's redemption that the Children of Jacob, who is Israel, came into Egypt before the Exodus that came to pass a few hundred years later.

The second Joseph that holds a major role in the biblical narrative is Joseph the husband of Mary the mother of Jesus. He appears in the books of Matthew, Mark, and Luke, which in parallel along with the book of John tell about the life and ministry of Jesus Christ. Joseph was betrothed to Mary when she became pregnant by the power of God, and he was faithful and obedient to God when he was directed to keep her, though he had in mind to divorce her when he learned she was pregnant before he had consummated their marriage. God spoke to Joseph in a dream. Joseph is not mentioned after Jesus' childhood, and presumably was not present for the ministry of the adult Christ.

There is also a minor character called Joseph of Aremethia who, after Jesus' crucifixtion, cared for the body of Jesus and gave a family tomb for the burial of his corpse. It turned out in Joseph's favor that Jesus only needed to "borrow" it for a few days.

There are 3 distinct (fairly) well-known Josephs in the Bible, firstly in the Old Testament (mainly):

1. Joseph the son of Jacob/Israel (aka The Patriarch Joseph). This Joseph is actually referred to in a few select places in the New Testament: John 4:5; Acts 7:9-18; Hebrews 11:21-22 & Revelation 7:8.

However, it's more likely that a Joseph in the New Testament would be one of:

2. Joseph husband of Mary and surrogate father of Jesus (aka St. Joseph).
3. Joseph of Arimathea in whose tomb Jesus was laid to rest.

There's also another 9 or 10 more obscure Josephs referred to in the Bible*, 4 more in the Old Testament*:

4. Father of Igal of the tribe of Issachar (cf. Numbers 13:7).
5. One of the "sons of Asaph" (cf. 1 Chronicles 25:2 & 9).
6. A descendant of Binnui, a contemporary of Ezra (cf. Ezra 10:38-42).
7. Head of the priestly family of Shekaniah, a contemporary of Nehemiah (cf. Nehemiah 12:14).

And 5 or 6 more in the New Testament:

8. One of the (half-)brothers of Jesus (often translated as "Joses" - cf. Mark 6:3).
9. The son of "Mary" and brother of James (possibly/probably The Mary, if so, identical to Joseph number 8. - cf. Mark 15:40 & 47).
10. The son of Mattathais (and father of Jannai) appearing in Luke's genealogy of Jesus (in which Joseph number 2. also appears - cf. Luke 3:24-25).
11. The son of Jonam (and father of Judah) also appearing in Luke's genealogy of Jesus (cf. Luke 3:30).
12. One of the nominees to replace Judas as an apostle, aka Barsabbas aka Justus (cf. Acts 1:23).
13. A Levite from Cyprus aka Barnabas who probably deserves to be listed amongst the "well-known" Josephs except that he is almost always referred to as Barnabas instead (cf. Acts 4:36).

*That is in the Protestant Canon, there are another 3 in the Deuterocanonical books: Son of Oziel (great-grandfather of Judith - cf. Judith 8:1); Son of Zechariah (cf. 1 Maccabees 5); Brother of Judas Maccabeus (aka John - cf. 2 Maccabees 8:22).