The current company I work for full-time, started off with me working as a contractor for them being paid hourly. About two years into working with them, the director of IT purchased a laptop for me on the company credit card to use for not only their development work, but also my schooling etc. When I graduated, they offered me a full-time position as a senior app developer at their company, so I brought my laptop (which they bought two years prior). The person who handled my on-boarding asked if they needed to purchase a laptop for me to use (clearly unaware my direct supervisor already purchased one for me 2 years ago) or if I had my own. I answered I had my own, and I did not need one from the company.
My question is, could I claim that laptop as my personal laptop? For example, if I was to leave this job, could I take this laptop with me?
I am also concerned that since I do a lot of extra contract work outside of my full-time job on this same laptop, they could potentially claim my extra projects as their property (This however is probably out of scope for workplace).
EDIT 1: All of our equipment(laptop, desktops, phones) given to employees has stickers/branding on it to help our IT department track where stuff is. My laptop does not have this.
EDIT2: I work for a medium sized company (100M Revenue), with an IT department of three people, including me. My boss is VP of IT who only reports to a hands off owner. I personally have known my boss since I was young, given that, I should probably just directly ask him and be done with it, but I was hoping to be less direct with my solution. I have also personally upgraded the laptop out of my own pocket when I was a contractor.