Head covering in puja is generally a matter of local tradition (maryāda), not a universal rule in Jain scriptures.

• What is common in many Śvetāmbara communities: it is customary for women to cover the head (using an odhni, pallu, or scarf) during pūjā, āratī, or pratikraman as a sign of modesty and respect. It is a community practice, not a strict doctrinal requirement for all followers. Follow your local sangh’s maryāda if they have guidelines.
• For men: the emphasis is on cleanliness and modesty; some communities prefer a simple upper-body cover or a dhoti with a shawl, but head-covering for men is not a universal rule.
• Digambar practice: ascetics have their own dress rules (monks are traditionally unclothed, nuns have their own observances). Among laypeople, head-covering is not a fixed doctrinal requirement but may appear as a regional/custom practice.

If you want, I can point you to temple-specific maryādā or dress guidelines in your area.

You can read more here and here