Ohm should not be spelled with an initial capital unless you are specifically talking about Mr. Georg Simon Ohm, or his Law. It's correct to say that a resistor value is 10 ohms (without the capital O).
When a unit is written as a single letter, the capital is used; for example, 10 µF (microfarads). There are exceptions: seconds should always use the lower-case letter: ps, ns, µs, ms, s, to distinguish them from siemens, the unit of conductance, which uses the upper-case letter. Times written with units of "µS" and "mS" are often seen, but are wrong.
The SI units for resistance should be written milliohm, ohm, kilohm (not kiloohm or kilo-ohm) and megohm (not megaohm or mega-ohm).
Other units that are named after people follow the same pattern:
picofarad, nanofarad, microfarad, millifarad, farad (named after Michael Faraday);
microvolt, millivolt, volt, kilovolt, megavolt (named after Alessandro Volta);
nanoamp, microamp, milliamp, amp (named after Ampere);
nanohenry, microhenry, millihenry, henry (named after Joseph Henry) (There doesn't seem to be a consensus on whether the plurals should be written microhenrys, etc, or microhenries, etc.)