Hehe, why do you think the gain will be changed ?:)
Omni in different settings, so for example V (normally) in horizontal position won't be omni in horizontal in my understanding. For example the antenna has horizontal beamwidth 360degrees (as normally omni should have) and 8 degrees in vertical. When you change it (rotate of 90 degrees), you will have 360 deg V and 8 deg H
Only panel antennas are reasonable to be rotated of 90 deg to change the polarization, there the H and V beamwidth are comparable.
If you need omni H, buy omni H, they are available on the market. Don't invent "new" antennas