Titles don't matter in the software engineer world. What matters most is your skills and experience.
Having a strong skills section, and a strong write up of your responsibilities will trump whatever silly title you were given. In fact you could have something like this:
June 2020-Present Company X, Developer
- Performed as a Full Stack Software Engineer by doing .....
- Did front end develop using .....
- Modified the xxx DB .....
- Created web services using .....
So I would be accurate with the job title, but you can easily overcome this by the rest of your resume.
An example of this is when works as a contractor. You are typically given a not very meaningful title, something like "developer" despite your pay rate being more than your manager's. One job I contracted at had me conducting the interviews, they did not trust their full time employees to do so.
In my almost 30 years experience I've never had a question come up about title, just my skills and abilities. This despite having some silly titles like "Programmer/Analyst" despite doing the work of a full stack developer.