I would say that everything is status quo now. The bill to confer SUSS its autonomous status needs to be passed in parliament first in order for SUSS to really be legally recognised in Singapore; apart from the private sector and also in all government sectors as I have heard that currently some statutory board still do not recognise 'UniSIM degree'. In a sense, the UniSIM name and branding still doomed the institution to a certain extent. People still have difficulty distinguishing SIM Global Education with SUSS (formally UniSIM). However, hopefully this will change in the days and years to come.
Right now in school, little seems to have changed externally apart from some UniSIM logo being taken off some posters. We still see the UniSIM logo in many places. The transformation is still quite stagnant and inconsistent. E.g. the notice board showed that UniSIM is part of the SIM group. Then we have the a notice that says 'UniSIM is now SUSS and is under the ambit of MOE'. Rather confusing at times for outsiders.
However, many students would have noticed that since one or two semesters ago, grading for assignments has become more stringent. Exams have also been tougher. Hence, although it seems like nothing has changed from the outside, the standard is picking up in the University itself. Looking back, the leading universities like NUS/NTU/SMU are not famous overnight. I believe they did gone through this budding phase like SUSS to reach their current status. For instance, NUS itself has over 100 years of history. After all, SUSS is considered a relatively new university with only 10 years of history. Hence, like what rabbit1 has mentioned, the level of recognition is definitely down the list now.
Nevertheless, I hope students and alumni can stop addressing SUSS as UniSIM to help the school to disengage SUSS from the SIM/ private university branding and smoothen its transition into Singapore's 6th University.