You could do it with a loop using $modx->user->isMember('groupname').
You could also use $modx->user->getMany(UserGroupMembers). That would give you an array of modUserGroupMember objects, one for each group the user belongs to.
http://bobsguides.com/modx-object-quick-reference.html#modUserGroupMember.
The usergroup ID for each group would be in the modUserGroupMember's user_group field. You'd then have to get each user group based on the ID, then get its name. It think the first method above would be faster but I'm not sure (and it would mean hard-coding the possible group names into the snippet).
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http://bobsguides.com/modx.html