|Mahmud||The praised one; variation of the name Muhammad|
|Mohammed||Praised; from Muhammad, name of the Prophet PBUH|
|Muhammad||Praised; name of the Prophet PBUH|
It is reported that the Prophet (peace be upon him) said: "On the Day of Resurrection, you will be called by your names and by your fathers' names, so give yourselves good names." (Hadith Abu Dawud)
Remember, just because a name stems from a certain language or culture, doesn't mean that it has a good Islamic meaning. Several of the companions of the Prophet Muhammad (peace be upon him) changed their own Arabic names, because the meanings of their names connoted wickedness.
For example, someone named Harb ("war") had his name changed to Silm ("peace"), and one named Al-Munba'ith ("one who lies") became Al-Mudtaji' ("one who stands up," i.e. for the truth).