There would be both copyright and trademark issues here. See U.S. Trademark Law - USPTO for law adn rules of practice related to US trademarks. See 17 USC for US copyright law.
Trademark
"Monopoly" is, I understand, protected as a trademark for a board game. It is currently owned by Hasbro. Any name which would be likely to confuse reasonable people into falsely thinking that the new game was authored or approved by the makers of the game Monopoly, or came from those makers would be trademark infringement (unless done by permission).
However, a name can allude to another name as long as no market confusion nor any dilution results. Under 15 U.S.C. § 1066 a mark which is "likely when used on or in connection with the goods or services of the applicant to cause confusion or mistake or to deceive." may be grounds for an interference which can prevent registration of the newer mark.
15 U.S.C. § 1125 provides that:
(a) (1) Any person who, on or in connection with any goods or services, or any container for goods,
uses in commerce any word, term, name, symbol, or device, or any combination thereof, or any false designation of origin, false or misleading description of fact, or false or misleading representation of fact, which—
(a) (1) (A) is likely to cause confusion, or to cause mistake, or to deceive as to the affiliation,
connection, or association of such person with another person, or as to the origin, sponsorship, or approval of his or her goods, services, or commercial activities by another person, or
(a) (1) (B) in commercial advertising or promotion, misrepresents the nature, characteristics, qualities, or geographic origin of his or her or another person’s goods, services, or commercial activities,
shall be liable in a civil action by any person who believes that he or she is or is likely to be damaged
by such act.
...
(c) Dilution by Blurring; Dilution by Tarnishment.--
(c) (1) Injunctive relief.--Subject to the principles of equity, the owner of a famous mark that is distinctive, inherently or through acquired distinctiveness, shall be entitled to an injunction
against another person who, at any time after the owner's mark has become famous, commences use of a mark or trade name in commerce that is likely to cause dilution by blurring or dilution by tarnishment of the famous mark, regardless of the presence or absence of actual
or likely confusion, of competition, or of actual economic injury.
(c) (2) Definitions.--(A) For purposes of paragraph (1), a mark is famous if it is widely recognized
by the general consuming public of the United States as a designation of source of the goods or services of the mark's owner. In determining whether a mark possesses the requisite degree of recognition, the court may consider all relevant factors, including the following:
(c) (2) (A) (1) (i) The duration, extent, and geographic reach of advertising and publicity of the mark, whether advertised or publicized by the owner or third parties.
(c) (2) (A) (1) (ii) The amount, volume, and geographic extent of sales of goods or services offered
under the mark.
(c) (2) (A) (1) (iii) The extent of actual recognition of the mark.
(c) (2) (A) (1) (iv) Whether the mark was registered under the Act of March 3, 1881, or the Act of
February 20, 1905, or on the principal register.
(c) (2) (B) For purposes of paragraph (1), `dilution by blurring' is association arising from the similarity between a mark or trade name and a famous mark that impairs the distinctiveness of the famous mark. In determining whether a mark or trade name is likely to cause dilution by blurring, the court may consider all relevant factors, including the following:
(c) (2) (B) (i) The degree of similarity between the mark or trade name and the famous mark.
(c) (2) (B) (ii) The degree of inherent or acquired distinctiveness of the famous mark.
(c) (2) (B) (iii) The extent to which the owner of the famous mark is engaging in substantially
exclusive use of the mark.
(c) (2) (B) (iv) The degree of recognition of the famous mark.
(c) (2) (B) (v) Whether the user of the mark or trade name intended to create an association with
the famous mark.
(c) (2) (B) (vi) Any actual association between the mark or trade name and the famous mark.
The word "Monopoly" as applied to games surely counts as a "famous martk" an so one must avoid confusion as well as "Dilution by Blurring". A game called "New Monopoly" is obviously intended to refer or allude to the existing game. Moreover it seems "intended to create an association with the famous mark" Such a mark might well constitute Dilution by Blurring. It might be wise to choose a name that is not as similar to the trademarked game, and is not as clearly and directly associated with the existing game. It might be wise to consult an experienced trademark lawyer as to whether any such name was close enough to an existing mark, particularly a famous one, to run a risk of a dilution or an infringement action.
One should note that a clear disclaimer, stating that a game is not affiliate with an existing game (or other product), and is not a product of that game's owners, nor approved or sponsored by those owners, can help avoid an infringement or dilution action.
Previous Suit
According to the Wikipedia article, "Monopoly (game)" (citations omitted):
Economics professor Ralph Anspach published Anti-Monopoly in 1973, and was sued for trademark infringement by Parker Brothers in 1974. The case went to trial in 1976. Anspach won on appeals in 1979, as the 9th Circuit Court determined that the trademark Monopoly was generic and therefore unenforceable. The United States Supreme Court declined to hear the case, allowing the appellate court ruling to stand. This decision was overturned by the passage of Public Law 98-620 in 1984. With that law in place, Parker Brothers and its parent company, Hasbro, continue to hold valid trademarks for the game Monopoly. However, Anti-Monopoly was exempted from the law and Anspach later reached a settlement with Hasbro and markets his game under license from them
Copyright
The concepts and procedures of a game, the so-called "game mechanics" cannot be protected by copyright. Specifically 17 USC 102(b) provides that:
(b) In no case does copyright protection for an original work of authorship extend to any idea, procedure, process, system, method of operation, concept, principle, or discovery, regardless of the form in which it is described, explained, illustrated, or embodied in such work.
So having a game in which tokens representing players move around a board, buying and selling properties, paying and collecting rents, and so on, is not protected by copyright. The artwork of any of the various editions of Monopoly would be protected by copyright, and may not be copied or imitated without permission. The layout of the board might be protected, depending on how original it is judged to be.
However, the original version on Monopoly called The landlord's Game dates from 1903, and any copyright in it has expired. Only new, original elements first published in 1925 or later would still be protected by copyright. Most of the layout elements are probably now in the public domain. Visual elements of modern editions may well still be under copyright.
Conclusion
Creation a new game that has some resemblance to Monopoly can probably be done without infringing any IP rights, but care would need to be taken to make it visually distinctive from any protected edition of the game. A name thatr was not similar enough to the existign name to involved "blurring" the existing trademark would need to be chosen. I am doubtful if "New Monopoly" is sufficiently distinctive.
