Islam forbids (knowingly) buying and possessing stolen property (Islam Q&A), while owning non-stolen property is allowed. Between these two extremes are:
Assumptions, where the Qur'an says:
O you who have believed, avoid much [negative] assumption. Indeed, some assumption is sin. ...
Suspicions, where we have the hadith:
Beware of suspicion, for suspicion is the worst of false tales ...
Sahih al-Bukhari 6064
Doubts, where we have the hadith:
... Leave what makes you in doubt for what does not make you in doubt. ...
Jami` at-Tirmidhi [grade: sahih]
From here, you'll need to determine you're making assumptions and are being suspicious, or if there is reasonable (and actionable) doubt. Basically, it boils down to Why do you think it's stolen? This may require interaction with a scholar.
In another context (halal vs. haram food), an Islam Q&A fatwa writes:
In ‘Awn al-Ma‘bood (9/2195-2196) it says: “Beware of suspicion” means: beware of following suspicion or beware of negative thinking, for suspicion is an accusation that comes to mind without any evidence.
Therefore, it's reasonable to believe that evidence is key in deciding whether or not these doubts are reasonable.