Before that it was primary residence since January 2019.Do I need to sell it this October to avoid capital gains tax to qualify for 2 of last 5 years exemption for capital gains (up to 250K single, 500K married filing jointly)?

When I move out in Sept, get married, and fill my current room, I'll basically be breaking even after expenses and maintenance.

If married, that would be a $1.5 million writeoff against your overall gains.  

The filing is a public record and when you file put maiden married etc. names DBA crazies.

I understand your apprehension about rates, but as the old adage goes you "marry the property but date the rate".

Realistically, I will be living in CA for the next ~5years; however, I'm not married to the area I'm currently living. 

If you owner occupy and rehab the home around you great while looking to sell at the 2 year and a day mark or later (to wash up to 250K as a single owner occupied/500K if married).  

The other option would be if there is a possibility for you to sell your primary residence and every two years move to one of the property and gradually sell each property once you get that tax exempt which is $250 thousand if single or $500 thousand is married.

I graduated back in May of 2022 and I am currently living with my beautiful fiancé and we are getting married in October.

So if you have 10 and you are married....then your spouse can have 10 as well.