Can I add ママ after any name and that will mean I'm referring to their mom?
Generally speaking, no. But people often drop の between nouns when it's an important and/or recurring concept to them. For example, when two people are casually talking about 木村さんのママ, they may start contracting it to 木村ママ during the conversation. In your case, 彼ママ is not a common phrase (I think I saw it for the first time today), but it's straightforwardly made from 彼(氏)のママ, and it's not difficult to grasp the intended meaning with the aid of the context.
By the way, ママ is occassionally used as a suffix for a real mother or someone with a mother-like character. For example 尾木直樹's nickname is 尾木ママ because of his character and feminine way of speaking. It's more like "Mother Ogi" rather than "Ogi's Mom".