Cancer cells are known for their ability to grow quickly and many people culture with a reduced serum and the reduced serum keeps them growing and dividing . for that i suggest The best thing you can do is plate out some wells of your cells and place different wells under different serum percentages and check to see how this effect in growth . This way you can get to know explanation of change in the growth pattern and morphology in your cell line and learn how they respond to serum changes .
Also , find the artical in attachment " Serum-dependent Growth Patterns of Two, Newly Established Human Mesothelioma Cell Lines1", where refer Julius Klominek, et al in that the choice of serum can affect the in vitro morphology of the established mesothelioma cell lines .
You can observe changes in cell growth if you change serum batch.
Usually not morphology changes if you use same serum type with same concentration.
You can have morphology changes if you use other specie serum or concentration like Saleh said or another choice is the your cells are infected by mycoplasma like Gabriel said.