Are there synonyms for "love marriage"?
Solution 1:
If I am understanding the term love marriage correctly, the closest English equivalent would be elope or elopement:
To elope, most literally, merely means to run away, and to not come back to the point of origination. More specifically, elopement is often used to refer to a marriage conducted in sudden and secretive fashion, usually involving hurried flight away from one's place of residence together with one's beloved with the intention of getting married. (Wikipedia)
The negative connotations I am hearing for love marriage is similar to the connotations of elopement. The idea of "running off together" is sending a rather strong message to your family and friends and stereotypically occurs when the couple do not have the blessing of their elders. Again stereotypically, the parents of the bride have taken issue with the groom. I do not know how often elopements actually occur or what the circumstances around them are.
The exact opposite of an elopement is referred to as a shotgun wedding:
A shotgun wedding is a form of forced marriage occasioned by an unplanned pregnancy. Some religions and cultures consider it a moral imperative to marry in such a situation, based on reasoning that premarital sex is sinful and unsafe. The phrase is an American colloquialism, though it is also used in other parts of the world. (Wikipedia)
As far as forced marriages go in stereotypical American society, a shotgun wedding is a close as it gets outside of extreme emotional or social coercion. When a shotgun wedding occurs, the bad reputation is still placed on the couple. Even the proverbial shotgun wielders are assumed justification for their actions.
Solution 2:
I've only ever heard "love marriage" in Indian contexts. In the US (I don't know about elsewhere), "marriage" by default is decided on by the couple, and any other method of decision (parents/relatives, church/community, etc (?)) is out of the mainstream, 'unorthodox', and so would would be needed to be marked as "arranged".
As to different regional variations on "arranged marriage", I don't know.
For "marriage" (which means "love marriage" to Indians), there are some slight variations here. There's "living together" which is an informal arrangement. There's "common-law marriage" which refers to the legal status of a couple who have been living together for long enough time to be considered married.
Solution 3:
"Love match" is a not uncommon phrase for a marriage without regard to prospects, money, etc. (The opposite, shown to perfection in Jane Austen, was sometimes called a "suitable marriage", but never an "arranged marriage", even if if had in fact been arranged by others.)