If I am running a multiple linear regression model with six independent variables against dependent variable, do the assumptions of multiple regression need to be satisfied?
or does this only applies if we are using the least squares method.
Yes, the assumptions should be satisfied in either of the cases. Typically it can be difficult to fulfill all the assumptions but the more assumptions are satisfied the more reliable the results become.
Here is a helpful link regarding the same: https://statistics.laerd.com/spss-tutorials/multiple-regression-using-spss-statistics.php