Is a belief that the Father, Son and Holy Spirit are not three persons, but one, Modalism? If I believe that the Father, the Son and the Holy Spirit are God, but not as three persons but as one, do I believe in Modalism?
Options to consider
In the history of conceptions regarding God, Jesus, and the Holy Spirit there have been names commonly assigned to some of them.  Over time, those named conceptions have developed a measure of stability and precision as shown in the Wikipedia entries dedicated to them.
A very good survey of non-Trinitarian conceptions can be found in the Wikipedia entry Nontrinitarianism.  Narrowing the field of options to those conceiving God the Father, Jesus, and the Holy Spirit as one person gives us a few options:

Monarchianism emphasizes God the Father as one, and this view has two types:

Modalistic monarchianism (or simply, Modalism), 'considers God to be one while appearing and working through the different &quot;modes&quot; of Father, Son, and Holy Spirit.'  This is the view of Oneness Pentecostalism.
Dynamic monarchianism (aka Adoptionism) conceives that God the Father &quot;adopted&quot; Jesus to be God at either baptism, resurrection, or ascension, and that Jesus remained divine since then.  In this view, Jesus is not co-eternal with the Father.  Viewed another way, Adoptionism is a kind of Subordinationism where Jesus has less status than the Father.  This is the view of the now extinct Ebionites and a few minor groups throughout history.


Unitarianism differs from Modalism that Unitarians teach that Jesus is not God, but an inspired man and a great teacher.  (see GotQuestions entry).  This is the view of the Unitarian churches, whose theology is described here.

Sabellianism is similar to Modalism in its conception.  Encyclopaedia Britannica characterizes it as a &quot;more developed and less naive form of Modalistic Monarchianism&quot;.  The different name is to identify the origin of the teaching as coming from Sabellius, a theologian and priest from the 3rd century, and as an Eastern Church heresy.  New World Encyclopedia has a good treatment on it.

Emanuel Swedenborg's view of the Trinity, expounded in Lee Woofenden's article Who is God? Who is Jesus Christ? What about that Holy Spirit?.  See also Mr. Woofenden's answer contrasting this view with modalism.


What you believe
Since you specify that 1) all three are God and 2) all three is one person, then what you believe can either be Modalistic monarchianism or Sabellianism or Swedenborg's view unless I failed to name other conceptions that can fit your search criteria.
Further study
One very good book about the historical development of the doctrine of Trinity, various ways of conceptualizing the Trinity, as well as practical consequences to other doctrines is The Trinity - A Guide for the Perplexed by an Anglican priest, Paul M. Collins, reviewed here.  Here's a relevant quote from Chapter 2 (Moments of Interpretation) in a section &quot;A pre-Nicene ecology of language&quot;:

Monarchianism can be said to have been used to safeguard the unity of God. Dynamic or adoptionist Monarchianism, attributed to Paul of Samosata, understood that the power (dynamis) of God had descended on Jesus, inspired him and given him divine honour. Some would argue that such an understanding can be read out of the Apostles’ Creed. There were other forms of Monarchianism: such as modalism, patripassianism and Sabellianism, in which the three names used in relation to the Godhead: Father, Son and Spirit represented one hypostasis or persona, which was manifest in a succession of modes. There was no understanding of any real distinction within
the divine being. These understandings of the divine led to the asking of crucial questions about how God in se was related to the revelation and redemption given. It is out of these concerns and the perceived threats of misunderstanding or heresy that the imperatives towards definition emerge.