As a general rule names cannot be subject to copyright, so you should be OK on that score. However names of people and characters can be trade marks, and if this is the case with the monster in question, you need look at the issue in relation your company name and what products or services your company provides.
The first thing to do is to check via the IPO website
if the monster's name is a registered trade mark. Using the link above, enter the name of the monster into the box marked 'Text' in the section named Trade Mark Text (second section down). Leave all the other entires as they are and click on 'Search' at the bottom of the form. Assuming any registrations do come up, make a note of all Status
, Nice Class
and Vienna Class
entries. Don't worry about what Nice and Vienna mean at this stage. As far as status is concerned you are only worried about those which are 'Registered' or 'New Applications'. The next thing to do is check which classes the various entries have been registered in. To do this click on the 'Classification' option on the left hand side of the page and when the page comes up, using the arrow to the right of the 'Class Number' box, select the class you want from the drop down list. Unfortunately you have to go this procedure for each separate class number. Click 'search', and then on the next page 'View Descriptions'. Look down the list of sub classes and note any categories which might include products or services your company deals in.
Having done all that for all registered marks bearing the relevant monster's name, if you have any matches between your company's products/services and those registered, you need to proceed to the next step.
Say that the name you searched for was 'Dracula' (there are 29 entries for this name) and in Class 33 you found this name was registered for 'alcoholic drinks', which your company also produces, you need to return to the listing of registrations (ie the result of your first search) and click on the actual registration number. This will take you to the details of the company which has registered the Trade Mark and more details about the registration. Taking my example, Trade Mark 2031063
is registered to Stephen Anton Komlosy for use with various beers, non-alcoholic and alcoholic beverages. If you make beer and use a name such as 'Drakula' then there is a very real chance of trade mark infringement due to having a similiar name applied to the same class of product.
If you find any clashes along the lines of my example, you need to either consider changing your company name or consult an IP lawyer about what else might be an option.