I am an formalist in the sense that I think that mathematics is just manipulation of symbols. But I think that this manipulation is motivated by the phantasy of humans: mathematical objects are for me created by human mind. What form of formalist am I?
The attitude you describe is the standard attitude of a working pure mathematician if you change a bit the weights: You can only do mathematics when you know about the semantics of your concepts.
Otherwise you make automatic theorem proving like a compiler :-)
Another answer is that you are not a formalist at all, but an intuitionist.
There is a range of positions between Platonism and formalism that we generally choose to ignore. To my mind, intuitionism is the most promising among them.
If you think many of these 'phantasies' constitute a shared factor in human experience, then they must reflect the composite intuition humans have developed to approach measurement and combination. In that case, they are not completely formal, but are based on something real.
Accepting that mathematical entities are not ideal objects, nor simply conventions that are entirely learned, but exist in the mind, and are a shared aspect of human experience makes mathematics an aspect of psychology. Its goal is to discern the shared structure of our common genetic mental inheritance and see how its contents combine.
Initially intuitionism was motivated by an approach to exploring the weakness in negation that causes Russel's paradox. The approach was to take negation itself as a psychological habit, and not a law of nature, or simply an aspect of grammar, and to look at other forms it takes in naive interpretations, in the hope of finding an improved habit that might be less audacious, but evade the defects.
Its originator was a good mathematician, but not very gifted philosopher, and expressed his intention very poorly. So very few people grasp the approach as an alternative view of mathematics, and instead see it as a precursor to constructivism, or a weird experiment in alternative logic.